**Exhibit 31.1****Section 302 Certification**I, David W. Sharp, certify that:     1. I have reviewed this quarterly report on Form 10-Q for the quarter ended September 30, 2006of Horizon Offshore, Inc.;     2. Based on my knowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this report;     3. Based on my knowledge, the financial statements, and other financial information includedin this report, fairly present in all material respects the financial condition, results ofoperations and cash flows of the registrant as of, and for, the periods presented in this report;     4. The registrant’s other certifying officer(s) and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and have:     (a) Designed such disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that material information relating tothe registrant, including its consolidated subsidiaries, is made known to us by others withinthose entities, particularly during the period in which this report is being prepared;     (b) Designed such internal control over financial reporting, or caused such internal controlover financial reporting to be designed under our supervision, to provide reasonable assuranceregarding the reliability of financial reporting and the preparation of financial statements forexternal purposes in accordance with generally accepted accounting principles;     (c) Evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of the disclosure controls andprocedures, as of the end of the period covered by this report based on such evaluation; and     (d) Disclosed in this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter (the registrant’sfourth fiscal quarter in the case of an annual report) that has materially affected, or isreasonably likely to materially affect, the registrant’s internal control over financialreporting; and     5. The registrant’s other certifying officer(s) and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and the auditcommittee 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 ofinternal control over financial reporting which are reasonably likely to adversely affect theregistrant’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 havea significant role in the registrant’s internal control over financial reporting.              /s/ David W. Sharp   David W. Sharp   President and Chief Executive OfficerHorizon Offshore, Inc.   Date: November 8, 2006