<PAGE>





                                                                    Exhibit 32.1

                           CERTIFICATIONS PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002



I, Robert E. Lee, President and Chief Executive Officer of Millennium Chemicals
Inc., certify that:

     1.  I have reviewed this annual report on Form 10-K of Millennium Chemicals
         Inc. as filed with the Securities and Exchange Commission on March 12,
         2004 and as amended by Form 10-K/A filed with the Securities and
         Exchange Commission on the date hereof;

     2.  Based on my knowledge, this annual report does not contain any untrue
         statement of a material fact or omit to state a material fact necessary
         to make the statements made, in light of the circumstances under which
         such statements were made, not misleading with respect to the period
         covered by this annual report;

     3.  Based on my knowledge, the financial statements, and other financial
         information included in this annual report, fairly present in all
         material respects the financial condition, results of operations and
         cash flows of the registrant as of, and for, the periods presented in
         this annual report;

     4.  The registrant's other certifying officers and I are responsible for
         establishing and maintaining disclosure controls and procedures (as
         defined in Exchange Act Rules 13a-15(e) and 15d-15(e) for the
         registrant and have:

            a)  designed such disclosure controls and procedures, or caused such
                disclosure controls and procedures to be designed under our
                supervision, to ensure that material information relating to the
                registrant, including its consolidated subsidiaries, is made
                known to us by others within those entities, particularly during
                the period in which this annual report is being prepared;

            b)  evaluated the effectiveness of the registrant's disclosure
                controls and procedures and presented in this report our
                conclusions about the effectiveness of the disclosure controls
                and procedures as of the end of the period covered by this
                report based on such evaluation; and

            c)  disclosed in this report any change in the registrant's internal
                control over financial reporting that occurred during the
                registrant's most recent fiscal quarter (the registrant's fourth
                fiscal quarter in the case of an annual report) that has
                materially affected, or is reasonably likely to materially
                affect, the registrant's internal control over financial
                reporting; and

     5.  The registrant's other certifying officers and I have disclosed, based
         on our most recent evaluation of internal controls over financial
         reporting, to the registrant's auditors and the audit committee of
         registrant's board of directors (or persons performing the equivalent
         functions):



<PAGE>


            a)  all significant deficiencies and material weaknesses in the
                design or operation of internal controls over financial
                reporting which are reasonably likely to adversely affect the
                registrant's ability to record, process, summarize and report
                financial information; and

            b)  any fraud, whether or not material, that involves management or
                other employees who have a significant role in the registrant's
                internal controls over financial reporting.


April 27, 2004
                                /s/ Robert E. Lee
                            ------------------------
                                  Robert E. Lee
                      President and Chief Executive Officer


                                       2