LYONDELL CHEMICAL COMPANY

12,000,000 SHARES OF COMMON STOCK

UNDERWRITING AGREEMENT

October 7, 2003

October 7, 2003

Credit Suisse First Boston LLC

Eleven Madison Avenue

New York, New York 10010-3629

Ladies and Gentlemen:

Lyondell Chemical Company, a Delaware corporation (the Company), proposes to issue and sell to Credit Suisse First Boston LLC (the Underwriter), an aggregate of 12,000,000 shares (the Underwritten Shares) and, at the election of the Underwriter, up to 1,800,000 additional shares (the Option Shares) of common stock, par value $1.00 per share (the Common Stock), of the Company. The Underwritten Shares and the Option Shares are herein referred to as the Shares. The Shares will have attached thereto share purchase rights (the Rights) issued pursuant to the Rights Agreement (the Rights Agreement) dated as of December 8, 1995 between the Company and The Bank of New York, as Rights Agent, as amended.

The Company has prepared and filed with the Securities and Exchange Commission (the Commission) in accordance with the provisions of the Securities Act of 1933, as amended, and the rules and regulations of the Commission thereunder (collectively, the Securities Act), a registration statement (the file number of which is 333-88348) on Form S-3, relating to the Common Stock and the related Rights and certain other equity and debt securities (the Shelf Securities) to be issued from time to time by the Company. The Company also has filed with, or proposes to file with, the Commission pursuant to Rule 424 under the Securities Act a prospectus supplement specifically relating to the Shares. The registration statement as amended to the date of this Agreement is hereinafter referred to as the Registration Statement and the related prospectus covering the Shelf Securities in the form first used to confirm sales of the Shares is hereinafter referred to as the Basic Prospectus. The Basic Prospectus as supplemented by the prospectus supplement specifically relating to the Shares in the form first used to confirm sales of the Shares is hereinafter referred to as the Prospectus. If the Company has filed an abbreviated registration statement pursuant to Rule 462(b) under the Securities Act (the Rule 462 Registration Statement), then any reference herein to the term Registration Statement shall be deemed to include such Rule 462 Registration Statement. Any

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reference in this Agreement to the Registration Statement, the Basic Prospectus, any preliminary form of Prospectus (a preliminary prospectus) previously filed with the Commission pursuant to Rule 424 or the Prospectus shall be deemed to refer to and include the documents incorporated by reference therein pursuant to Item 12 of Form S-3 under the Securities Act which were filed under the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission thereunder (collectively, the Exchange Act) on or before the date of this Agreement or the date of the Basic Prospectus, any preliminary prospectus or the Prospectus, as the case may be; and any reference to amend, amendment or supplement with respect to the Registration Statement, the Basic Prospectus, any preliminary prospectus or the Prospectus shall be deemed to refer to and include any documents filed under the Exchange Act after the date of this Agreement, or the date of the Basic Prospectus, any preliminary prospectus or the Prospectus, as the case may be, which are deemed to be incorporated by reference therein.

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