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                                                                    Exhibit 31.1

                      CERTIFICATION 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.;

     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 years presented in
          this annual report;

     4.   The registrant's other certifying officer 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 year 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 last fiscal quarter 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 officer and I have disclosed, based
          on our most recent evaluation of internal control over financial
          reporting, to the registrant's auditors and the audit committee of the
          registrant's board of directors (or persons performing the equivalent
          functions):

               a)   all significant deficiencies and material weaknesses in the
                    design or operation of internal control 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 control over financial reporting.

Date: March 12, 2004


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