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                                                                    EXHIBIT 31.1

CERTIFICATION

I, Wilfred J. Corrigan, certify that:

     1.   I have reviewed this quarterly report on Form 10-Q of LSI Logic
          Corporation;

     2.   Based on my knowledge, this 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 report;

     3.   Based on my knowledge, the financial statements, and other financial
          information included in this 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
          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 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 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:

                    (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: November 12, 2003

By:    /s/ Wilfred J. Corrigan
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Name:  Wilfred J. Corrigan
Title: Chairman & Chief Executive Officer