Exhibit 99.1

EXECUTION COPY

FIRST SUPPLEMENTAL INDENTURE

This FIRST SUPPLEMENTAL INDENTURE, dated as of August 20, 2010 (this “Supplemental Indenture”), is executed by and between AMERICREDIT SYNDICATED WAREHOUSE TRUST, a Delaware statutory trust (together with its successors and assigns, the “Issuer”) and WELLS FARGO BANK, NATIONAL ASSOCIATION, as trustee and trust collateral agent (in such capacities, together with its successors and assigns, the “Trustee”). Capitalized terms used, but not otherwise defined herein, shall have the meanings ascribed thereto in the Indenture.

WITNESSETH:

WHEREAS, the Issuer, the Trustee and the Administrative Agent are parties to that certain Indenture, dated as of February 26, 2010 (the “Indenture”);

WHEREAS, subject to the terms and conditions set forth herein, the parties hereto have agreed to amend certain provisions of the Indenture as described below;

NOW, THEREFORE, in consideration of the premises and the mutual agreements hereinafter set forth, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

Section 1. Amendment to the Indenture. Effective as of the date first above written and subject to the satisfaction of the conditions precedent set forth in Section 2 below, the Indenture is hereby amended as follows:

1.1. The definition of “Change of Control” set forth in Annex A to the Indenture is hereby amended and restated in its entirety as follows:

“Change of Control” means a change resulting when:

(A) any Unrelated Person or any Unrelated Persons, acting together, that would constitute a Group together with any Affiliates or Related Persons thereof (in each case also constituting Unrelated Persons) shall at any time either (i) Beneficially Own more than 30% of the aggregate voting power of all classes of Voting Stock of AmeriCredit Corp. or (ii) succeed in having sufficient of its or their nominees elected to the Board of Directors of AmeriCredit Corp. such that such nominees when added to any existing director remaining on the Board of Directors of AmeriCredit Corp. after such election who is an Affiliate or Related Person of such Person or Group, shall constitute a majority of the Board of Directors of AmeriCredit Corp.; provided, that notwithstanding the foregoing, a “Change of Control” shall not occur if on or prior to December 31, 2010, General Motors Company, together with any Affiliates or Related Persons, shall, pursuant to that certain Agreement and Plan of Merger, dated as of July 21, 2010 among General Motors Holdings LLC, Goalie Texas Holdco Inc. and AmeriCredit Corp. (x) Beneficially Own more than 30% of the aggregate voting power of all classes of Voting Stock of AmeriCredit Corp. or (y) succeed in having sufficient of its or their nominees elected to the Board of Directors of AmeriCredit Corp. such that such nominees when added to any existing director remaining on the Board of Directors of AmeriCredit Corp. after such election who is an Affiliate or Related Person of such Persons, shall constitute a majority of the Board of Directors of AmeriCredit Corp.; or

(B) (x) Leucadia National Corporation and any Affiliates or (y) Fairholme Funds, Inc., Fairholme Capital Management, L.L.C. (on behalf of those advisory accounts, other than Fairholme Funds, Inc., included as restricted persons) and any Affiliates (collectively, the “Leucadia/Fairholme Entities”) shall at any time Beneficially Own more than 40% of the aggregate voting power of all classes of Voting Stock of AmeriCredit Corp.

As used herein, (a) “Beneficially Own” shall mean “beneficially own” as defined in Rule 13d-3 of the Exchange Act, or any successor provision thereto; provided, however, that, for purposes of this definition, a Person shall not be deemed to Beneficially Own securities tendered pursuant to a tender or exchange offer made by or on behalf of such Person or any of such Person’s Affiliates until such tendered securities are accepted for purchase or exchange; (b) “Group” shall mean a “group” for purposes of Section 13(d) of the Exchange Act; (c) “Unrelated Person” shall mean at any time any Person other than the Leucadia/Fairholme Entities, AmeriCredit Corp. or any of its Subsidiaries, any of the shareholders of AmeriCredit Corp. on March 8, 2002 and other than any trust for any employee benefit plan of AmeriCredit Corp. or any of its Subsidiaries; (d) “Related Person” of any Person shall mean any other Person owning (1) 5% or more of the outstanding common stock of such Person or (2) 5% or more of the Voting Stock of such Person; and (e) “Voting Stock” of any Person shall mean the capital stock or other indicia of equity rights of such Person which at the time has the power to vote for the election of one or more members of the Board of Directors (or other governing body) of such Person.

Section 2. Conditions Precedent. This Supplemental Indenture shall become effective as of the date above written upon satisfaction of the following conditions precedent: (a) the Administrative Agent and the Trustee shall have received executed counterparts of this Supplemental Indenture duly executed by the parties hereto; (b) the Administrative Agent and the Trustee shall have confirmed to its satisfaction that the Issuer (or AmeriCredit on behalf of the Issuer) shall have provided written notice to the Rating Agency of the execution and delivery of this Supplemental Indenture and (c) all fees, expenses and other amounts due and payable on the date hereof by AmeriCredit or the Issuer to the Administrative Agent, the Agents or the Noteholders shall have been paid in full.

Section 3. Issuer Orders; Noteholder Instructions.

3.1. By execution hereof, each of the Issuer and the Noteholders party hereto, constituting the Required Noteholders, hereby authorize, instruct and direct the Trustee to execute this Supplemental Indenture and further authorizes, instructs and directs the Trustee to execute this Supplemental Indenture without receiving an Officer’s Certificate or an Opinion of Counsel. Each of the undersigned Noteholders hereby represents and warrants that (i) it is a beneficial owner of the Notes issued pursuant to the Indenture or (ii) it is the nominee or advisor for the beneficial owner indicated, and that the beneficial owner has granted to the undersigned the power and authority to deliver this Supplemental Indenture on behalf of such beneficial owner and such power and authority has not been revoked.

3.2. By execution hereof, each of the Noteholders party hereto, constituting the Required Noteholders, hereby consent to the execution and delivery by the Issuer, the Sellers, the Servicer, the Administrative Agent, the Backup Servicer and the Trust Collateral Agent of an amendment to the definition of “Change of Control” set forth on Annex A to the Sale and Servicing Agreement consistent with the terms set forth in Section 1 of this Supplemental Indenture, and authorize, instruct and direct the Trustee to execute such amendment to the Sale and Servicing Agreement without receiving an Officer’s Certificate or an Opinion of Counsel.

Section 4. Representations and Warranties. The Issuer hereby represents and warrants that: (a) it has the power and is duly authorized to execute and deliver this Supplemental Indenture; (b) the

2

execution and delivery of this Supplemental Indenture has been duly authorized by all actions necessary on its part; (c) this Supplemental Indenture and the Indenture as amended hereby, constitute legal, valid and binding obligations of the Issuer and are enforceable against the Issuer in accordance with their terms; and (d) immediately prior, and after giving all effect, to this Supplemental Indenture, no event, condition or circumstance has occurred and is continuing which constitutes a Default or an Event of Default.

Section 5. Entire Agreement. The parties hereto hereby agree that this Supplemental Indenture constitutes the entire agreement concerning the subject matter hereof and supersedes any and all written and/or oral prior agreements, negotiations, correspondence, understandings and communications.

Section 6. Effectiveness of Supplemental Indenture. Except as expressly amended by the terms of this Supplemental Indenture, all terms and conditions of the Indenture shall remain in full force and effect and are hereby ratified and confirmed. This Supplemental Indenture is effective only for the specific purpose for which it is given and shall not operate as a consent, waiver, amendment or other modification of any other term or condition set forth in the Indenture or any right, power or remedy of any Noteholder under the Indenture. Upon the effectiveness of this Supplemental Indenture, each reference in the Indenture to “this Indenture” or words of like import shall mean and be references to the Indenture as amended hereby, and each reference in any other Basic Document to the Indenture or to any terms defined in the Indenture which are modified hereby shall mean and be references to the Indenture or to such terms as modified hereby.

Section 7. Limitation of Liability. Notwithstanding anything contained herein to the contrary, this Agreement has been executed by Wilmington Trust Company, not in its individual capacity but solely in its capacity as Owner Trustee of the Issuer and in no event shall Wilmington Trust Company in its individual capacity or, except as expressly provided in the Trust Agreement, as Owner Trustee have any liability for the representations, warranties, covenants, agreements or other obligations of the Issuer hereunder or in any of the certificates, notices or agreements delivered pursuant hereto, as to all of which recourse shall be had solely to the assets of the Issuer. For all purposes of this Agreement, in the performance of its duties or obligations hereunder or in the performance of any duties or obligations of the Issuer hereunder, the Owner Trustee shall be subject to, and entitled to the benefits of, the terms and provisions of Articles V, VI and VII of the Trust Agreement. Notwithstanding anything contained herein to the contrary, this Agreement has been executed and delivered by Wells Fargo Bank, National Association, not in its individual capacity but solely as Trustee and in no event shall Wells Fargo Bank, National Association, have any liability for the representations, warranties, covenants, agreements or other obligations of the Issuer hereunder or in any of the certificates, notices or agreements delivered pursuant hereto, as to all of which recourse shall be had solely to the assets of the Issuer. In no event shall Wells Fargo Bank, National Association, in any of its capacities hereunder, be deemed to have assumed any duties of the Owner Trustee under the Delaware Statutory Trust Act, common law, or the Trust Agreement.

Section 8. Fees, Costs and Expenses. AmeriCredit shall pay on demand all reasonable and invoiced fees and out-of-pocket expenses of Sidley Austin LLP, counsel for the Administrative Agent and the Agents, incurred in connection with the preparation, negotiation, execution and delivery of this Supplemental Indenture.

Section 9. GOVERNING LAW. THIS SUPPLEMENTAL INDENTURE WILL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK (WITHOUT REFERENCE TO THE CONFLICT OF LAW PRINCIPLES THEREOF OTHER THAN SECTIONS 5-1401 AND 5-1402 OF THE NEW YORK GENERAL OBLIGATIONS LAW) AND THE OBLIGATIONS, RIGHTS AND REMEDIES OF THE PARTIES HEREUNDER SHALL BE DETERMINED IN ACCORDANCE WITH SUCH LAWS.

3

Section 10. Severability. In case any provision in this Supplemental Indenture will be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions will not in any way be affected or impaired thereby.

Section 11. Binding Effect. This Supplemental Indenture shall be binding upon and shall be enforceable by parties hereto and their respective successors and permitted assigns.

Section 12. Novation. This Supplemental Indenture does not constitute a novation or termination of the Indenture or any Basic Document and all obligations thereunder are in all respects continuing with only the terms thereof being modified as provided herein.

Section 13. Counterparts. This Supplemental Indenture may be executed in any number of counterparts, each of which so executed will be deemed to be an original, but all such counterparts will together constitute but one and the same instrument.

4

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed and delivered by their respective authorized officers as of the date first above written.

Signature Page to First Supplemental Indenture

The undersigned, constituting the Required Noteholders, hereby

consent to this First Supplemental Indenture

as of the date first above written:

Signature Page to First Supplemental Indenture

Signature Page to First Supplemental Indenture