CHUYS OPCO, INC. c/o Goode Partners LLC 667 Madison Avenue, 21st Floor New York, New York 10021 November 7, 2006

Exhibit 10.9

CHUY’S OPCO, INC.

c/o Goode Partners LLC

667 Madison Avenue, 21^st Floor

New York, New York 10021

November 7, 2006

Three Star Management, Ltd.

1623 Toomey Road

Austin, Texas 78704

Attention: Michael R. Young / John A Zapp

Gentlemen:

This letter agreement (this “Agreement”) sets forth our mutual understanding with respect to the proposed development of the Arbor Trails Chuy’s (as defined herein) and is delivered pursuant to the terms of that certain Asset Purchase Agreement dated as of the date hereof (the “Purchase Agreement”), by and among the undersigned (the “Company”), Three Star Management, Ltd. (“Developer”) and the other parties thereto. Capitalized terms used but not defined in this Agreement have the meanings assigned to them in the Purchase Agreement.

MY/ZP IP Group, Ltd., a Texas limited partnership formerly known as Chuy’s-Comida Deluxe, Inc. and affiliated with Developer (“IP Group”), will assign to an affiliated Texas limited partnership to be formed (the “Landlord Entity”) that certain Contract for Sale (the “Land Contract”) between IP Group and CP Austin Forum 71, L.P., a Texas limited partnership (“CP Austin”) for the purchase of Lot 4, Block A, Arbor Trails Subdivision, a subdivision in the City of Austin, Travis County, Texas, according to the map or plat recorded as Document Number 200500129, in the Official Public Records of Travis County (the “Land”). The Land Contract obligates CP Austin to process applications for, and use diligent efforts to obtain, the approval of all applicable governmental authorities and/or private entities so as to authorize the construction of a Chuy’s restaurant on the Land (the “Arbor Trails Chuy’s”). The Land is encumbered by various restrictions that regulate exterior colors, materials, signs, height and other matters pertaining to the improvements that may be built upon the Land (the “Site Restrictions”).

Subject to (a) CP Austin’s satisfaction of all conditions precedent under, and performance of its obligations under, the Land Contract, and (b) the Landlord Entity’s receipt of all necessary approvals to build the Arbor Trails Chuy’s, each of which approvals shall be in a form satisfactory to Developer, in its sole discretion (including without limitation building permits, sign permits, site development permits, curb cut

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November 7, 2006

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approvals, construction plan approvals and architectural approvals from all applicable governmental authorities and/or private persons or entities) and of construction bids for the construction of and installation of all fixtures, furniture and equipment in, the Arbor Trails Chuy’s, all in amounts acceptable to Developer, in its sole discretion (collectively, the “Acquisition Conditions”), and with the caveat that the Site Restrictions may require modification of the exterior of the Arbor Trails Chuy’s from the look of other “ground up” constructed units owned by the Seller Group and in operation as of the date hereof (the “Other Units”), Developer will take all action reasonably necessary or proper to cause the Landlord Entity to deliver the Arbor Trails Chuy’s to the Company as a “turn-key” operation with the look, quality and fixtures of the completed Arbor Trails Chuy’s substantially similar to the look, quality and fixtures of the Other Units, except as may be required by the Site Restrictions, all as more particularly set forth in the Lease (defined below). Developer will have the right to terminate this Agreement by notice to the Company if the Acquisition Conditions are not satisfied in Developer’s sole discretion; provided, however, that if the unsatisfied Acquisition Condition(s) are unacceptable based solely on increases in the anticipated cost of delivering the Arbor Trails Chuy’s in the condition required by this Agreement, and if the Company agrees to pay the excess cost in a manner reasonably satisfactory to Developer, upon mutual execution of agreements that require the Company to pay such excess cost, this Agreement will continue in force and effect. The package of furniture, fixtures and equipment to be delivered pursuant to this paragraph (the “FF&E”) shall be as set forth on Annex A attached hereto.

The parties expect the Arbor Trails Chuy’s to be completed on or about the third quarter of 2007, but the Company acknowledges that this is an estimate and agrees that there will be no penalty to Developer or the Landlord Entity if completion of the Arbor Trails Chuy’s is delayed or accelerated. Developer or the Landlord Entity will bear all costs associated with the initial construction of the Arbor Trails Chuy’s and the installation of the FF&E therein. These costs will include sales taxes, ad valorem taxes during the period of construction, permitting fees, development fees, and the costs of labor, materials and acquisition and installation of the FF&E. As among Developer, Landlord Entity and the Company, prior to the Delivery Date (defined below) the Landlord Entity will be responsible for all liability related to or arising out of the development, construction and physical condition of the Arbor Trails Chuy’s. The Landlord Entity will assign to the Company all construction and FF&E warranties upon the Delivery Date and thereafter the Company will be responsible for all costs of maintenance, repair, ownership and/or occupancy of the Arbor Trails Chuy’s. The Company also will be responsible for procuring all food and beverage items, all costs relating to the hiring and training of personnel or advertising related to the opening of the location, and all other costs of operating the restaurant and for all costs set forth in the Lease.

On the Delivery Date, the Landlord Entity and the Company will enter into a lease of the Land (the “Lease”) in substantially the form attached hereto as Annex B. Upon substantial completion of the Arbor Trails Chuy’s, the Landlord Entity will deliver to the

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Company a written notice advising the Company that the Arbor Trails Chuy’s is substantially complete (the “Inspection Notice”) and that a certificate of occupancy has been issued by the applicable governmental authorities. The Company will have 15 Business Days from its receipt of the Inspection Notice to inspect the Arbor Trails Chuy’s and to request correction of any defects in materials or workmanship (“Defects”). Following correction of any Defects, the Landlord Entity will deliver to the Company a written notice of completion of the Arbor Trails Chuy’s and of tender of delivery of the Arbor Trails Chuy’s (the “Completion Notice”), together with two (2) counterparts of the Lease, executed by the Landlord Entity. Within 5 Business Days following receipt of the Completion Notice, the Company will deliver to the Landlord Entity an executed counterpart to the Completion Notice (the “Acknowledgement”) and one fully executed counterpart to the Lease. The Delivery Date shall occur, and rent will begin to accrue under the Lease, on the earlier of (i) the date the Company opens the Arbor Trails Chuy’s for business or (ii) 5 Business Days after delivery by the Company of an executed counterpart of the Completion Notice.

Not later than 15 Business Days following the first Business Day of the seventeenth month of continuous operation of the Arbor Trails Chuy’s by the Company, the Company will, or will cause its independent accounting firm to, prepare and deliver to the Developer a statement (the “Statement”) setting forth the trailing 12-month store level EBITDAT for the Arbor Trails Chuy’s (the “Profit Calculation”). The Profit Calculation will be prepared in a manner consistent with those accounting practices used to evaluate EBITDA for Chuy’s of Shenandoah, Ltd in the financial statement and projections attached hereto as Annex C. If the Developer has any objections to the Profit Calculation, it will deliver a detailed statement (the “Statement of Objections”) describing its objections to the Company within 30 calendar days of its receipt of the Statement. If the Developer fails to notify the Company of any such dispute within such 30-calendar day period, the Statement delivered to it will be deemed to be the “Final Statement.” The Developer and the Company will use commercially reasonable efforts to resolve any such objections, and each party will (i) provide the other party and its Representatives with full access during normal business hours to the books and records related to the Profit Calculation and (ii) fully cooperate with all reasonable requests by the other party in connection with such party’s review of the Profit Calculation, the Statement and the Statement of Objections.

If a final resolution with respect to the Profit Calculation is not obtained within 30 calendar days after the Company has received the Statement of Objections, the Developer and the Company will mutually appoint a nationally recognized accounting firm independent of the Landlord Entity, Developer and the Company (the “Accounting Referee”) to review the final Profit Calculation proposed by each party (each, a “Final Offer”). If the parties fail to select the Accounting Referee within 10 Business Days after the expiration of the 30-calendar day negotiation period, either the Landlord Entity, on behalf of itself and Developer, or the Company may request JAMS to appoint an independent firm of certified public accountants to perform the services required by the Accounting Referee.

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Each party will cooperate with the Accounting Referee and provide the Accounting Referee with information reasonably requested by it and necessary to assess the final offers. The decision of the Accounting Referee as to which Final Offer is equal to or closest to the actual trailing 12-month store level profit of the Arbor Trail’s Chuy’s as determined by the Accounting Referee will be final and binding on all parties (the “Final Determination”). The fees and expenses of the Accounting Referee and the fees of JAMS, as applicable, will be paid by the party whose Final Offer is the furthest from the Final Determination.

Once the Profit Calculation has been finalized in accordance with the terms herein, the Company will pay to you by wire transfer of immediately available funds to a bank account designated by you an amount (the “Purchase Price”) equal to the Profit Calculation multiplied by four (4). From and after the date the Company takes possession of the Arbor Trails Chuy’s, except for its obligations to pay the Purchase Price, the Company will have all right, title and interest to the profits of the Arbor Trails Chuy’s and will be responsible for any losses resulting from the operation of the Arbor Trails Chuy’s. Title to the FF&E will transfer to the Company upon payment of the Purchase Price pursuant to an “as is” bill of sale.

Each of the Developer and the Landlord Entity will use, and cause its Affiliates to use, commercially reasonable efforts in the performance of their obligations hereunder and under the Lease, as applicable. The quality of the development services provided by Developer hereunder will be substantially equivalent to the quality of development services historically provided by you with respect to the development of the Other Units (the Company acknowledging that the obligation to obtain approvals for the development is the obligation of CP Austin and not within Developer’s control).

To the maximum extent permitted by Law, Developer will indemnify, hold harmless, protect and defend (with counsel acceptable to the Company) the Company and its officers, directors, employees, agents and contractors, from and against any and all claims, demands, actions, fines, penalties, liabilities, losses, damages, injuries and expenses (including, without limitation, actual attorneys’, consultants’ and expert witnesses’ fees and costs at the pre-trial, trial and appellate levels, on a full indemnity basis) in any manner related to, arising out of or in connection with: (a) the willful misconduct or gross negligence by the Developer, the Landlord Entity, or the agents or employees or either Developer or the Landlord Entity in the performance of Developer’s obligations under this Agreement; and (b) any failure to perform Developer’s obligations under this Agreement to the extent such failure was within Developer’s control, and subject in all events to the Acquisition Conditions.

To the maximum extent permitted by Law, the Company will indemnify, hold harmless, protect and defend (with counsel acceptable to Developer) Developer and its officers, directors, employees, agents and contractors, from and against any and all claims, demands, actions, fines, penalties, liabilities, losses, damages, injuries and

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expenses (including, without limitation, actual attorneys’, consultants’ and expert witnesses’ fees and costs at the pre-trial, trial and appellate levels, on a full indemnity basis) in any manner related to, arising out of or in connection with any failure to perform the Company’s obligations under this Agreement to the extent such failure was within the Company’s control, and subject in all events to the Acquisition Conditions.

The provisions set forth in Article VIII of the Purchase Agreement are incorporated herein by reference and apply to this Agreement mutatis mutandis.

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If this accurately reflects your understanding, please execute two copies of this Agreement.

Signature Page Arbor Trails Letter Agreement