AMENDMENT NO. 4 TO UNDERTAKING AGREEMENT

Exhibit 4.23(d)

AMENDMENT NO. 4 TO UNDERTAKING AGREEMENT

AMENDMENT dated as of August 3, 2006 to the Undertaking Agreement dated as of December 17, 2003 (as heretofore amended, 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 (as amended, 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. Amendments. (a) Section 1.01 of the Undertaking Agreement is hereby amended by inserting the following definitions therein in correct alphabetical order:

“Permitted LCR Acquisition” means the acquisition by Lyondell, directly or indirectly, of the 41.25% equity interest in LCR which, at the date hereof, was not owned by it.

“Permitted LCR Sale” means (i) any sale or other disposition of all (but not less than all) of Lyondell’s direct or indirect ownership interest in LCR, provided that the net cash proceeds of such sale are used to prepay Indebtedness of Lyondell in compliance with the provisions of Section 3.12(b) or (ii) any sale or other disposition of all or substantially all of the assets of LCR, provided that the net proceeds of such sale or disposition in excess of amounts required to satisfy Indebtedness or other obligations of LCR are promptly distributed to the holders of equity interests in LCR and the portions thereof received by Lyondell or a Subsidiary (net of any applicable taxes) are used to prepay Indebtedness of Lyondell in compliance with the provisions of Section 3.12(b).

(b) The following definition in Section 1.01 of the Undertaking Agreement is amended to read in its entirety as follows:

“JV Subsidiaries” means each Subsidiary of Lyondell that directly holds an equity interest in any Lyondell Joint Venture.

(c) The proviso to Section 3.09 of the Undertaking Agreement is hereby amended by adding the phrase “other than a CA Obligor” immediately preceding the words “to incur”.

(d) Section 3.16 of the Undertaking Agreement is hereby amended by adding the following paragraph at the end thereof:

Notwithstanding the foregoing, the obligations relating to LCR set forth in this Section (and elsewhere in the Transaction Documents) shall no longer apply following consummation of a Permitted LCR Sale and application of the proceeds thereof.

(e) Section 3.19 of the Undertaking Agreement is hereby amended by adding the phrase “and a Permitted LCR Acquisition” immediately after the phrase “Lyondell’s acquisition of Millennium” in clause (iv) to the proviso thereto.

(f) For the avoidance of doubt, simultaneously with the consummation of a Permitted LCR Acquisition, then for all purposes of the Undertaking Agreement LCR shall cease to be a Lyondell Joint Venture and the Subsidiaries of Lyondell that hold an equity interest in LCR shall cease to be JV Subsidiaries.

SECTION 3. 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.

SECTION 4. Governing Law. This Amendment shall be governed by and construed in accordance with the laws of the State of New York.

SECTION 5. 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 6. Effectiveness. This Amendment shall become effective on the date (the “Amendment Effective Date”) when 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

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party). 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.

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