OCCIDENTAL PETROLEUM CORPORATION

Exhibit 1.2

OCCIDENTAL PETROLEUM CORPORATION

October 7, 2003

Credit Suisse First Boston LLC

Eleven Madison Avenue

New York, New York 10010-3629

Ladies and Gentlemen:

This letter agreement (the “Agreement”) is being executed in order to document our understanding regarding the purchase by us or one of our affiliates from you in a public offering (the “Public Offering”) of registered shares of common stock, par value $1.00 per share (the “Original Common Stock”), of Lyondell Chemical Company, a Delaware corporation (the “Company”).

The Company proposes to issue and sell to you, and you propose to offer, an aggregate of 12,000,000 shares (the “Underwritten Shares”) and, at your election, up to 1,800,000 additional shares (the “Option Shares” and together with the Underwritten Shares, the “Shares”) of Original Common Stock, pursuant to an underwriting agreement, between the Company and you entered into concurrently with this Agreement (the “Underwriting Agreement”). As of the date of this Agreement, excluding 5,000,000 shares of Original Common Stock issuable upon exercise of a warrant, we beneficially own 36,310,792 shares of the Company’s Series B common stock (the “Series B Common Stock”, and together with the Original Common Stock, the “Common Stock”), which represents approximately 22% of the Company’s common equity. Unless otherwise provided herein, capitalized terms used and not defined herein shall have the meanings ascribed to them in the Underwriting Agreement.

Subject to the terms and conditions of this Agreement and the closing of the sale of the Underwritten Shares on the Closing Date, we agree to purchase from you, in the Public Offering, 2,700,000 shares of Original Common Stock (the “Oxy Shares”) on the Closing Date at the Purchase Price per share specified in the Underwriting Agreement. Notwithstanding the foregoing, you shall have no obligation to sell to us any Oxy Shares in the event the Underwriting Agreement is terminated (for any reason) or in the event the Company fails to deliver such shares to you, it being understood that the Company shall not be deemed to have delivered any Oxy Shares on the Closing Date until the Company shall have first delivered 9,300,000 Underwritten Shares on the Closing Date.

This Agreement is made in reliance upon our representations and warranties to you contained in this Agreement. We hereby represent and warrant to you that the Oxy Shares to be acquired by us will be acquired for investment for our own account, not as a nominee or agent, and not with a view to the resale or distribution of any part thereof, and that in connection with the Public Offering, we will comply with the provisions of Regulation M under the Securities Exchange Act of 1934, as amended. By executing this Agreement, we further represent and warrant to you that we do not presently have any contract, undertaking, agreement or arrangement with any person to sell, transfer or grant participations to such person or to any third person with respect to, any of the Oxy Shares.

We hereby agree on behalf of ourselves and our direct and indirect subsidiaries (collectively, the “Restricted Parties”), that from the date hereof and until 90 days after the public offering date set forth in the final prospectus used to sell the Shares (the “Public Offering Date”) pursuant to the Underwriting Agreement, the Restricted Parties will not offer, sell, contract to sell, pledge or otherwise dispose of, directly or indirectly, any shares of Common Stock or securities convertible into or exchangeable or exercisable for any shares of Common Stock, enter into a transaction which would have the same effect, or enter into any swap, hedge or other arrangement that disposes of, in whole or in part, any of the economic consequences of ownership of shares of Common Stock, whether any such aforementioned transaction is to be settled by delivery of shares of Common Stock or such other securities, in cash or otherwise, or publicly disclose the intention to make any such offer, sale, pledge or disposition, or to enter into any such transaction, swap, hedge or other arrangement, without, in each case, your prior written consent; provided, however, that the foregoing restrictions shall not prevent Occidental

from making public statements concerning its long term expectations for its investment in the Company so long as Occidental does not state any specific plan or proposal to sell. In addition, we agree that, without your prior written consent, the Restricted Parties will not, during the period commencing on the date hereof and ending 90 days after the Public Offering Date, make any demand for or exercise any right with respect to, the registration of any shares of Common Stock or any security convertible into or exercisable or exchangeable for shares of Common Stock. Any shares of Common Stock received upon exercise of warrants or the payment of in-kind dividends will also be subject to the foregoing restrictions of this paragraph. The foregoing restrictions of this paragraph shall not apply to our purchase of shares of Original Common Stock in open market transactions after the Closing Date pursuant to Section 2.2(b) of the Stockholders Agreement among the Company and the Stockholders named therein, dated August 22, 2002.

In furtherance of the foregoing, the Company and its transfer agent and registrar are hereby authorized to decline to make any transfer of shares of Common Stock if such transfer would constitute a violation or breach of this Agreement.

If the Underwriting Agreement is terminated for any reason, this Agreement (including, without limitation, our obligations in the second immediately preceding paragraph) shall also terminate at the time of such termination. You shall have no liability to the undersigned arising out of any termination of the Underwriting Agreement or the failure to consummate the transaction contemplated therein and the undersigned acknowledges that you have the right to terminate the Underwriting Agreement and/or to decline to consummate the transaction contemplated therein under certain circumstances. This Agreement shall be binding on us and our successors and assigns.

This Agreement shall be governed by and construed in accordance with the laws of the State of New York (without reference to the choice of law rules thereof).

Accepted as of the date hereof:

CREDIT SUISSE FIRST BOSTON LLC