Exhibit 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Millennium Chemicals Inc. (the
"Company") on Form 10-K for the year ending December 31, 2003 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Robert
E. Lee, President and Chief Executive Officer of the Company, certify, pursuant
to 18 U.S.C. 'SS'1350, as adopted pursuant to 'SS'906 of the Sarbanes-Oxley
Act of 2002, that:

     (1) The Report fully complies with the requirements of Section 13 or 15(d)
of the Securities Exchange Act of 1934; and

     (2) The information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of the
Company.

Date: March 12, 2004


                                                    /s/ ROBERT E. LEE
                                         ---------------------------------------
                                                      Robert E. Lee
                                         President and Chief Executive Officer

This certification, which is required by Section 906 of the Sarbanes-Oxley Act
of 2002, is "furnished" to the Securities and Exchange Commission in accordance
with Item 601(b)(32)(ii) of Regulation S-K, 17 CFR 229.601(b)(32)(ii).