Exhibit 99.3

Red Robin Gourmet Burgers, Inc.

6312 South Fiddlers Green Circle, # 200N

Greenwood Village, CO 80111

April 5, 2011

Oak Street Capital Management, LLC

111 South Wacker Drive, 33rd floor

Chicago, IL 60606

Dear Sirs:

This letter constitutes the agreement (the “Agreement”) among David Makula (“Mr. Makula”) and Oak Street Capital Management, LLC (“Oak Street”), each on behalf of itself and its affiliated funds, persons and entities, both current and future, including without limitation Mr. Makula and the other persons listed on Schedule 1 hereto (collectively, the “Investor Group”), and Red Robin Gourmet Burgers, Inc., a Delaware corporation (the “Company”).

WHEREAS, on March 10, 2011, Oak Street, on behalf of the record stockholder indicated therein, sent a letter (the “Nomination Letter”) to the Company stating its intention to nominate two (2) directors to the board of directors of the Company (the “Board”).

WHEREAS, the Company and Investor Group have agreed that it is in their mutual interests to enter into this Agreement, among other things, to set forth certain agreements concerning the composition of the Board and other corporate governance matters, as hereinafter described.

NOW, THEREFORE, in consideration of the promises and the representations, warranties and agreements contained herein, and other good and valuable consideration, the parties hereto mutually agree as follows:

1. As promptly as practicable following the date of this Agreement (but in no event later than April 12, 2011), the Board shall, pursuant to the powers granted to the Board under Article II of the Bylaws of the Company (the “Bylaws”), increase the size of the Board to eleven and appoint Mr. Makula as a Class I director of the Company to fill the new directorship so created on the Board and to serve in such capacity until the 2012 annual meeting of the stockholders of the Company (the “2012 Meeting”).

(a) Without limiting the previous paragraph, Mr. Makula agrees to serve as a director of the Company through at least December 31, 2011, unless he becomes unable to do so due to injury, illness, death or similar circumstance. If Mr. Makula becomes unable to serve as a director of the Company due to injury, illness, death or other similar circumstance on or before December 31, 2011, or if Mr. Makula leaves the Board after

April 5, 2011

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December 31, 2011 for any reason prior to the end of his then-current term, Oak Street shall be entitled to recommend to the Board one or more replacement directors, to serve in succession (each, a “Replacement Director”). The Board may withhold approval of any Replacement Director recommended by Oak Street; provided, however, that such approval shall not be unreasonably withheld. In the event that the Board does not accept a Replacement Director recommended by Oak Street, Oak Street shall have the right to recommend additional Replacement Directors for consideration by the Board. The Board shall, no later than five business days after the Board’s approval of such Replacement Director, appoint such Replacement Director to the Board as a Class I director to serve until the end of the then-current term of such Replacement Director’s predecessor.

(b) If the Investor Group is not in material breach of this Agreement and Mr. Makula or the then-current Replacement Director is serving as a director at the time, then, in its sole discretion of the Board, the Board may nominate (or re-nominate) Mr. Makula or the then-current Replacement Director for election (or re-election) at the 2012 Meeting.

(c) No later than April 12, 2011, Mr. Makula shall be appointed to the Audit Committee of the Board. In addition, Mr. Makula shall be appointed to any special committee of the Board (“Committee”) that is created after the date hereof for the purpose of considering strategic alternatives of the Company (including without limitation, a sale, merger, disposition of all or substantially all of the Company’s assets, or financing involving a strategic change in the Company’s financing strategy). Subject to Section 1(a) of this Agreement, if Mr. Makula or the then-current Replacement Director leaves the Board for any reason prior to the end of his then-current term, the Replacement Director appointed pursuant to Section 1(a) shall replace such Replacement Director’s predecessor and, assuming such Replacement Director meets the applicable qualifications necessary to serve on any such committee, shall continue to serve on any committee on which such predecessor served immediately prior to his departure from the Board for the remainder of such predecessor’s then-current term.

2. If at any time during the Support Period (defined below), any member of the Investor Group materially breaches the terms of this Agreement, Mr. Makula or the then-current Replacement shall resign from the Board within five days thereafter, and the Investor Group shall have no further rights under Section 1 of this Agreement to designate any member of the Board.

3. Each member of the Investor Group shall (a) in the case of all shares of the Company’s Common Stock (the “Common Stock”) owned of record by it as of the record date for the 2011 Annual Meeting (the “Record Date”), and (b) in the case of all shares of the Common Stock beneficially owned by any member of the Investor Group as of the Record Date (whether held in street name or by some other arrangement), instruct the record holder to: in each case at the 2011 Annual Meeting, (i) publicly support and vote for the election of each of Steve Carley, Pattye Moore and Marcus Zanner or such other director nominees as are supported by the Board; (ii) vote to abstain or against any shareholder nominations for director or shareholder proposals (whether made pursuant to Rule 14a-8 or Rule 14a-4 under the Securities Exchange Act of 1934, as amended (the “Exchange Act,” and such proposals, “Shareholder Proposals”)) that are not approved and recommended by the Board, (iii) publicly support and

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vote for ratification of the Company’s auditors for the 2011 fiscal year, and (iv) publicly support and vote for the proposal to approve an amendment to the Company’s equity incentive plan.

4. Except for the Investor Group’s agreement to support the Company’s nominees and proposals described in this Agreement, from the date of this Agreement until the date immediately following the day on which the 2012 Meeting is held or, if later, such date that is five months following the latest date on which either Mr. Makula or the then-current Replacement Director is a director of the Company (the “Support Period”), no member of the Investor Group shall, and will cause its affiliates not to, directly or indirectly:

(a) make, or in any way participate, directly or indirectly, in any “solicitation” (as such term is used in the proxy rules of the Securities and Exchange Commission (the “SEC”)) of proxies or consents, conduct or suggest any binding or nonbinding referendum or resolution or seek to advise, encourage or influence any individual, partnership, corporation, limited liability company, group, association or entity (collectively, a “Person”) with respect to the voting of any of the Common Stock;

(b) initiate, propose or otherwise “solicit” (as such term is used in the proxy rules of the SEC) shareholders of the Company for the approval of shareholder proposals or cause or encourage any person to initiate any such shareholder proposal;

(c) propose or nominate, or cause or encourage any person to propose or nominate, any candidates to stand for election to the Board, or seek the removal of any member of the Board;

(d) except as previously disclosed in the Investor Group’s Schedule 13D filings, form, join or otherwise participate in a “partnership, limited partnership, syndicate or other group” within the meaning of Section 13(d)(3) of the Exchange Act (other than the group already formed among the Investor Group) with respect to the Common Stock or deposit any shares of Common Stock in a voting trust or similar arrangement or subject any shares of Common Stock to any voting agreement or pooling arrangement, or grant any proxy with respect to any shares of Common Stock (other than to a designated representative of the Company pursuant to a proxy statement of the Company);

(e) take any public action to act alone or in concert with others to control or seek to control, or to influence or seek to influence, the management, the Board or the policies of the Company;

(f) seek to call, or to request the call of, or call a special meeting of the shareholders of the Company, or make a request for a list of the Company’s shareholders or other Company records;

(g) otherwise take, or solicit, cause or encourage others to take (or disclose publicly or in a manner that could reasonably be expected to become public, any intention to take) any action inconsistent with any of the foregoing;

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(h) acquire, offer or propose to acquire, or agree to acquire (except by the way of stock dividends, stock splits, reverse stock splits or other distributions or offerings made available to holders of shares of Common Stock generally), whether by purchase, tender or exchange offer, through the acquisition of control of another Person, by joining a partnership, limited partnership, syndicate or other group (as defined under Section 13(d) of the Exchange Act) or otherwise, any shares of Common Stock if, as a result of such acquisition, the members of the Investor Group would beneficially own in the aggregate in excess of 16.5% of the then outstanding shares of Common Stock; or

(i) publicly, or in a manner that could reasonably be expected to become public, seek to amend or request a waiver of any of the foregoing.

For the avoidance of doubt, any actions of Mr. Makula or the then-current Replacement Director taken in his capacity as a member of the Board shall not be deemed to violate the foregoing clauses (a) through (i).

5. During the Support Period, no member of the Investor Group shall, and each of them shall not solicit, cause or encourage others to, make any comments or statements regarding the Company or its current or former officers, directors or employees, which are derogatory or detrimental to, or which disparage, any of the Company or its current or former officers, directors or employees, provided, however, that nothing in this Agreement to the contrary shall prohibit the Investor Group from (i) making public statements (including statements contemplated by Rule 14a-1(1)(2)(iv) under the Exchange Act), (ii) engaging in discussions with other stockholders or (iii) soliciting, or encouraging or participating in the solicitation of, proxies or consents with respect to voting securities of the Company (so long as such discussions are in compliance with subsection 4(d) hereof) in each case with respect to any transaction that has been publicly announced by the Company involving (1) the recapitalization of the Company, (2) an acquisition, disposition or sale of assets or a business by the Company where the consideration to be received or paid in such transaction requires approval by the holders of the Common Stock or (3) a change of control of the Company. During the Support Period, neither the Company nor any of its officers or directors shall, nor shall any of them solicit, cause or encourage others to, make any comments or statements regarding the Investor Group or any of their respective partners, officers, directors or employees, which are derogatory or detrimental to, or which disparage, any of them. The foregoing shall not apply to compelled testimony, either by legal process, subpoena or otherwise, or to communications that are required by an applicable fiduciary or legal obligation and are subject to contractual provisions providing for confidential disclosure.

6. Effective as of the date of this Agreement, Oak Street hereby withdraws the Nomination Letter. Further, effective as of the date of this Agreement, Oak Street hereby represents to the Company that Oak Street is dissolving the group of Reporting Persons formed with Kovitz Investment Group and its affiliates.

7. The Company shall issue a press release substantially in the form attached hereto as Exhibit A (the “Press Release”) as soon as practicable on or after the date hereof, but in no event later than April 7, 2011 and the Company shall file a corresponding Form 8-K that includes both the Press Release and this Agreement. As soon as practicable on or after the date hereof, but in no event later than April 7, 2011, the Investor Group shall file a corresponding

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amendment to its Schedule 13D. Neither the Company nor the Investor Group shall make any public announcement or statement that is inconsistent with or contrary to the statements made in the Press Release, except as required by law or the rules of any stock exchange or with the prior written consent of the other party. Each member of the Investor Group represents and warrants to the Company that it is unaware of any fact or circumstance that would require them to make any such disclosure.

8. Mr. Makula and each Replacement Director and each of their affiliates shall comply with those policies and procedures of the Company applicable to members of the Board of Directors and affiliates of such persons that are currently in effect or that may be in effect from time to time.

9. The Company and the members of the Investor Group each acknowledge and agree that (a) a breach or a threatened breach by either party may give rise to irreparable injury inadequately compensable in damages and accordingly each party shall be entitled to injunctive relief, without proof of actual damages, to prevent a breach or threatened breach of the provisions hereof and to enforce specifically the terms and provisions hereof in any state or federal court having jurisdiction, (b) neither party shall plead in defense for any such relief that there would be an adequate remedy at law, (c) any applicable right or requirement that a bond be posted by either party is waived and (d) such remedies shall not be the exclusive remedies for a breach of this Agreement, but will be in addition to all other remedies available at law or in equity. The members of the Investor Group understand and acknowledge that the United States securities laws prohibit any person who has material, non-public information from purchasing or selling securities of a company to which such information relates or from communicating such information to any other person or entity under circumstances in which it is reasonably foreseeable that such person or entity is likely to purchase or sell such securities.

10. All notices and other communications under this Agreement shall be in writing and shall be given (and shall be deemed to have been duly given upon receipt) by delivery in person or by facsimile, or by Federal Express or registered or certified mail, postage pre-paid, return receipt requested, as follows:

If to the Company:

Red Robin Gourmet Burgers, Inc.

6312 South Fiddlers Green Circle, #200N

Greenwood Village, CO 80111

Attn: General Counsel

with a copy (which shall not constitute notice) to:

Ronald R. Levine, II, Esq.

Davis Graham & Stubbs LLP

1550 17th Street, Suite 500

Denver, CO 80202

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Page 6

If to Oak Street:

Oak Street Capital Management, LLC

111 South Wacker Drive, 33rd floor

Chicago, IL 60606

Attn: David Makula

with a copy (which shall not constitute notice) to:

Drinker Biddle & Reath LLP

191 North Wacker Drive

Suite 3700

Chicago, IL 60606

Attn: Jeffrey Blumberg, Esq.

11. This Agreement may be executed by the signatories hereto in separate counterparts, each of which when so executed and delivered shall be an original, but all such counterparts shall together constitute one and the same instrument.

12. This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without regard to its conflict of laws principles. The parties hereto consent to exclusive jurisdiction and venue in any action to enforce this Agreement in any court of competent jurisdiction located in Wilmington, Delaware.

13. This Agreement constitutes the only agreement between the Investor Group and the Company with respect to the subject matter hereof and supersedes all prior agreements, understandings, negotiations and discussions whether oral or written. This Agreement shall inure to the benefit of the parties hereto and their respective successors and permitted assigns. This Agreement may not be assigned by any party without the express written consent of the other party. No amendment, modification, supplement or waiver of any provision of this Agreement may in any event be effective unless in writing and signed by the party or parties affected thereby.

14. The Company represents and warrants that (a) the Company has the power and authority to execute, deliver and carry out the terms and provisions of this Agreement and to consummate the transactions contemplated hereby, and (b) this Agreement has been duly and validly authorized, executed and delivered by the Company, constitutes a valid and binding obligation and agreement of the Company and is enforceable against the Company in accordance with its terms.

15. Oak Street represents and warrants that (a) it has the power and authority to execute, deliver and carry out the terms and provisions of this Agreement and to consummate the transactions contemplated hereby, and (b) this Agreement has been duly and validly authorized, executed and delivered by Oak Street, constitutes a valid and binding obligation and agreement of Oak Street and is enforceable against Oak Street in accordance with its terms.

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16. The Company shall be responsible for reimbursing the Investor Group for its reasonable and documented travel and legal (for services actually rendered, and not for retainers) expenses incurred by the Investor Group prior to the date hereof in connection with the investment by the Investor Group in the Company, provided that in no event shall the Company be required to reimburse the Investor Group an amount more than $62,500.

[signature page follows]

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Accepted and agreed to:

Schedule 1

Oak Street Capital SPV 1 LP

Oak Street Capital Master Fund, Ltd.

Patrick Walsh

Exhibit A

Red Robin Appoints David Makula to the Board of Directors

Signs Support Agreement with Oak Street Capital Management

Greenwood Village, Colo. – April 5, 2011 –Red Robin Gourmet Burgers, Inc., (NASDAQ: RRGB) today announced the appointment of David Makula, the Managing Member and Chief Investment Officer of Oak Street Capital Management, LLC (“Oak Street”), to its Board of Directors. The Company also announced it has signed a “Support Agreement” with Oak Street in conjunction with Mr. Makula’s appointment to the Board. Under the terms of the Support Agreement, Oak Street has agreed to support Red Robin’s anticipated proposals at the 2011 Annual Meeting and to a number of “standstill” agreements through the day following the 2012 Annual Meeting.

“I’m pleased to welcome David to the Red Robin Board of Directors and I look forward to his future contributions to Red Robin,” said Pattye Moore, Red Robin’s independent Board Chair. “With David’s appointment, we have now added five new independent directors in the last year, as well as our new CEO, Steve Carley, substantially enhancing the quality of our corporate governance. We are also making great strides strategically and operationally as we continue to focus intensely on our strategic plan, Project RED. The Board will continue to work very closely with management to maximize the benefits associated with our plan to drive long-term shareholder value.”

“I’m very pleased to join the Red Robin Board of Directors and look forward to contributing to the Board’s effort to drive long-term shareholder value,” said Mr. Makula.

Mr. Makula founded Oak Street, one of the largest beneficial owners of Red Robin stock, in 2005, and continues to serve as its Managing Member and Chief Investment Officer. Oak Street manages fundamentally-driven investment portfolios for institutional and high net worth investors. Mr. Makula has gained significant experience in the restaurant industry through Oak Street’s investments. Previously, Mr. Makula participated in the management of a $700 million Chicago-based investment firm. Mr. Makula began his career as a Mergers & Acquisitions investment banker at Salomon Smith Barney in New York, New York. He holds a B.S. in Accountancy from the University of Illinois at Urbana-Champaign, graduating with high honors. He is also a Certified Public Accountant.

The Company will increase the size of the Board to 11 members with the appointment of Mr. Makula as a Class I director. Oak Street has agreed to withdraw its separate nomination of Mr. Makula and Patrick Walsh to the board of directors and to support our nominees at the upcoming Annual Meeting.

About Red Robin Gourmet Burgers, Inc. (NASDAQ: RRGB)

Red Robin Gourmet Burgers, Inc. (www.redrobin.com), a casual dining restaurant chain founded in 1969 that operates through its wholly-owned subsidiary, Red Robin International, Inc., serves up wholesome, fun, feel-good experiences in a family-friendly environment. Red Robin®

restaurants are famous for serving more than two dozen insanely delicious, high-quality gourmet burgers in a variety of recipes with Bottomless Steak Fries®, as well as salads, soups, appetizers, entrees, desserts, and signature Mad Mixology® Beverages. There are more than 450 Red Robin® restaurants located across the United States and Canada, including company-owned locations and those operating under franchise agreements.

For further information contact:

ICR

Don Duffy/Raphael Gross

203-682-8200