Exhibit 4.26(a)

AMENDMENT NO. 1 TO UNDERTAKING AGREEMENT

AMENDMENT dated as of June 25, 2004 to the Undertaking Agreement dated as of December 17, 2003 (the “Undertaking Agreement”) by LYONDELL CHEMICAL COMPANY, a Delaware corporation (“Lyondell”), in favor of the PURCHASERS (as defined in the Receivables Purchase Agreement dated as of December 17, 2003 (the “Receivables Agreement”) among Lyondell Funding II, LLC, as Seller, Lyondell, as Servicer, the Purchasers from time to time party thereto and Citicorp USA, Inc., as asset agent and administrative agent (the “Agent”) for the Purchasers) and CITICORP USA, INC., as Agent.

The parties hereto agree as follows:

SECTION 1. Defined Terms; References. Unless otherwise specifically defined herein, each term used herein which is defined in the Undertaking Agreement, or incorporated by reference therein, has the meaning assigned to such term in the Undertaking Agreement or so incorporated. Each reference to “hereof”, “hereunder”, “herein” and “hereby” and each other similar reference and each reference to “this Agreement” and each other similar reference contained in the Undertaking Agreement shall, after this Amendment becomes effective, refer to the Undertaking Agreement as amended hereby.

SECTION 2. Amended Definitions. (a) The following definitions in Section 1.01 of the Undertaking Agreement are amended to read in their entirety as follows:

“Acquisition” means the acquisition by Lyondell, directly or indirectly, of ARCO Chemical and of Millennium.

“Distributable Cash Flow” means with respect to any Lyondell Joint Venture or non-wholly owned Subject Assets Transferee for any period, an amount equal to the lesser of “A” or “B” where:

“A” equals the greater of (i) zero and (ii) Lyondell’s direct and/or indirect share of the cash from operations (as defined in accordance with GAAP and adjusted to exclude the effect of any extraordinary gain or loss) of such Person for such period minus Lyondell’s direct and/or indirect share of the gross capital expenditures of such Person for such period; and

“B” equals the greater of (i) zero and (ii) cash distributions by such Person to Lyondell or a JV Subsidiary during such period (including repayment of Investments made in such Person by Lyondell or a Subsidiary) less the aggregate amount of Investments made by Lyondell or a Subsidiary in such Person during such period (other than Investments permitted by clause (B) of Section 3.19 and clause (ii) of the proviso to

Section 3.19). For purposes of calculations hereunder, Investments made within 45 days after the end of a Fiscal Year as contemplated by clause (i) of the proviso to Section 3.19 shall be deemed made during such preceding Fiscal Year.

(b) Clause (c) of Section 1.02 of the Undertaking Agreement is hereby amended by deleting the word “and” in the parenthetical phrase therein, inserting a comma in place thereof, and inserting the phrase “and (iii) the acquisition of Millennium” at the end of such parenthetical phrase.

SECTION 3. Amendments to Article 3. (a) Clause (b) of Section 3.13 of the Undertaking Agreement is hereby amended by adding the phrase “to the extent permitted by Section 3.19” at the end thereof.

(b) Article 3 of the Undertaking Agreement is hereby amended by adding new Section 3.19 as follows:

Section 3.19. Investments in Lyondell Joint Ventures. Lyondell will not, and will not permit any Subsidiary to, make any Investment in any Lyondell Joint Venture if (i) at the time thereof or immediately after giving effect thereto, a Potential Event of Termination or Event of Termination would exist or (ii) if the aggregate amount of such Investments made on and after July 1, 2004 would exceed the sum of (A) $100,000,000 plus (B) the aggregate net cash proceeds of Equity Issuances on or after July 1, 2004 (other than any Equity Issuance the Net Cash Proceeds of which have been or will be used to make a prepayment of Debt pursuant to Section 3.12); provided that (i) Lyondell and its Subsidiaries may make Investments in any Lyondell Joint Venture during any Fiscal Year or within 45 days after the end of such Fiscal Year in amounts that, together with all other Investments made in such Lyondell Joint Venture in respect of such Fiscal Year in reliance on this proviso during such Fiscal Year or within 45 days after the end of such Fiscal Year, do not exceed the amount of dividends or distributions previously paid in respect of such Fiscal Year to Lyondell or any Subsidiary by such Lyondell Joint Venture and (ii) Lyondell may issue shares of its common stock upon conversion of Millennium’s 4.000% Convertible Debentures due 2023 (and amounts of Investments permitted by this proviso shall not be taken into account for purposes of clauses (A) and (B)). For the purposes of calculations under clause (i) of the preceding proviso, Investments made within 45 days after the end of a Fiscal Year shall be deemed made during such preceding Fiscal Year.

SECTION 4. Representations of Lyondell. Lyondell represents and warrants that (i) the representations and warranties of Lyondell set forth in Article 2 of the Undertaking Agreement and Article IV of the Receivables Agreement will be true in all material respects on and as of the Amendment Effective Date (as defined below) with the same effect as though made on and as of such date, except to the extent such representations and warranties expressly relate to an earlier date and (ii) no Potential Event of Termination or Event of Termination will have occurred and be continuing on such date.

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SECTION 5. Governing Law. This Amendment shall be governed by and construed in accordance with the laws of the State of New York.

SECTION 6. Counterparts. This Amendment may be signed in any number of counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

SECTION 7. Effectiveness. This Amendment shall become effective on the first date when, and simultaneously with the time upon which, the following conditions are met (the “Amendment Effective Date”):

(a) the Agent shall have received counterparts hereof signed by each of the Required Purchasers and Lyondell (or, in the case of any party as to which an executed counterpart shall not have been received, the Agent shall have received in form satisfactory to it facsimile or other written confirmation from such party of execution of a counterpart hereof by such party); and

(b) Lyondell’s acquisition of Millennium shall have been consummated.

Promptly after the Amendment Effective Date occurs, the Agent shall notify Lyondell and the Purchasers thereof, and such notice shall be conclusive and binding on all parties hereto.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the date first above written.

LYONDELL CHEMICAL COMPANY
By:	/s/ Karen A. Twitchell
Name:	Karen A. Twitchell
Title:	Vice President and Treasurer

Citicorp USA, Inc.
By:	/s/ David Jaffe
Name:	David Jaffe
Title:	Vice President

BANK OF AMERICA, N.A.
By:	/s/ Kevin R. Kelly
Name:	Kevin R. Kelly
Title:	Senior Vice President

CREDIT SUISSE FIRST BOSTON, ACTING THROUGH ITS CAYMAN ISLANDS BRANCH
By:	/s/ Peter Chauvin
Name:	Peter Chauvin
Title:	Vice President
By:	/s/ David Dodd
Name:	David Dodd
Title:	Associate

Bank One, N.A.
By:	/s/ J. Devin Mock
Name:	J. Devin Mock
Title:	Director

NATIONAL CITY BUSINESS CREDIT, INC.
By:	/s/ Michael S. Fine
Name:	Michael S. Fine
Title:	Director

WELLS FARGO FOOTHILL, LLC
By:	/s/ Mike Baranowski
Name:	Mike Baranowski
Title:	Vice President

The Bank of New York
By:	/s/ Raymond J. Palmer
Name:	Raymond J. Palmer
Title:	Vice President

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