AMENDMENTNO. 2 TO AMENDED AND RESTATED CREDIT AGREEMENT

EXHIBIT 4.8(b)

[CONFORMED COPY]

AMENDMENT NO. 2 TO AMENDED AND

RESTATED CREDIT AGREEMENT

AMENDMENT dated as of May 13, 2003 to the Amended and Restated Credit Agreement dated as of June 27, 2002 (as heretofore amended, the “Credit Agreement”) among LYONDELL CHEMICAL COMPANY, a Delaware corporation (the “Borrower”); the LENDERS from time to time party thereto; BANK OF AMERICA, N.A. and CITIBANK, N.A., as Co-Syndication Agents; SOCIETE GENERALE and UBS WARBURG LLC, as Co-Documentation Agents; and JPMORGAN CHASE BANK, as administrative agent (in such capacity, the “Administrative 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 Credit Agreement has the meaning assigned to such term in the Credit Agreement. 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 Credit Agreement shall, after this Amendment becomes effective, refer to the Credit Agreement as amended hereby.

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

“Capital Expenditures” means, for any Person for any fiscal period, the additions to property, plant and equipment and other capital expenditures of the Borrower and its Consolidated Subsidiaries for such period, as the same are (or would in accordance with GAAP be) set forth in a statement of cash flows of such Person for such period; provided that “Capital Expenditures” shall exclude (i) expenditures required, mandated or necessary to comply with the laws, rules, regulations or other requirements of any governmental authority, (ii) expenditures of property and casualty insurance or any award or other compensation with respect to any condemnations of property (or any transfer or disposition of property in lieu of condemnation) and related insurance deductibles, (iii) expenditures incurred in connection with the conversion of the Borrower’s MTBE facilities to produce other gasoline blending components in an aggregate amount not exceeding $85,000,000 for all fiscal periods and (iv) Specified Business Acquisitions; and provided further that “Capital Expenditures” shall include (without duplication) Investments made in the

PO-11 JV or the PO-12 JV during such fiscal period to finance Capital Expenditures of such Borrower Joint Ventures.

“Specified Business Acquisition” means (i) the acquisition in whole or in part by the Borrower or any of its Subsidiaries of a butanediol production facility in Botlek, The Netherlands (known as BDO-2), whether by acquisition of securities, property or assets, (ii) the acquisition by the Borrower of the interests of Occidental Petroleum Corporation in Equistar pursuant to the transactions described in the Information Memorandum or (iii) the acquisition by the Borrower or any of its Subsidiaries of additional interests in Equistar, either directly or through the acquisition of wholly-owned Subsidiaries that own such interest either directly or indirectly through wholly-owned Subsidiaries, so long as any such acquisition under clause (ii) or (iii) hereof is in exchange for common equity securities of the Borrower (or cash funded by a substantially simultaneous sale of common equity securities of the Borrower to the seller or an affiliate of the seller).

(b) The figure “$3,050,000,000” in the definition of Senior Notes is changed to “$3,250,000,000.”

SECTION 3. Covenant Amendment. Section 5.15(b) of the Credit Agreement is amended to read in its entirety as follows:

(b) Prior to the Mandatory Prepayment Release Date, neither the Borrower nor any Subsidiary will optionally prepay, redeem, purchase, acquire or make any other principal payment in respect of any Debt, including any refinancing thereof, other than (i) the Loans, (ii) Working Capital Facilities, (iii) intercompany Debt, (iv) the Senior Notes from Net Cash Proceeds and Excess Cash Flow Prepayment Amounts to the extent that those Net Cash Proceeds and Excess Cash Flow Prepayment Amounts are not applied to prepayment of the Term Loans pursuant to Section 2.04(c) by reason of Section 2.04(e) thereof, (v) the Senior Notes to the extent of any amount that is offered in prepayment, and is not applied to prepayment, of the Term Loans pursuant to Section 2.09(d) and (vi) Debt related to the acquisition described in clause (i) of the definition of Specified Business Acquisition.

SECTION 4. Representations of Borrower. The Borrower represents and warrants that (i) the representations and warranties of the Borrower set forth in Article 4 of the Credit 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

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warranties expressly relate to an earlier date and (ii) no Default will have occurred and be continuing on such date.

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 (the “Amendment Effective Date”) when the Administrative Agent shall have received counterparts hereof signed by each of the Required Lenders and the Borrower (or, in the case of any party as to which an executed counterpart shall not have been received, the Administrative 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).

Promptly after the Amendment Effective Date occurs, the Administrative Agent shall notify the Borrower, the other Agents and the Lenders 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.