**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 period ended September 30,2007 of Horizon Offshore, Inc.;           2. Based on my knowledge, this report does not contain any untrue statement of amaterial fact or omit to state a material fact necessary to make the statements made, in light ofthe circumstances 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 informationincluded in this report, fairly present in all material respects the financial condition, resultsof operations and cash flows of the registrant as of, and for, the periods presented in thisreport;           4. The registrant’s other certifying officer(s) and I are responsible for establishingand maintaining 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 ActRules 13a-15(f) and 15d-15(f)) for the registrant and have:           (a) Designed such disclosure controls and procedures, or caused suchdisclosure controls and procedures to be designed under our supervision, toensure that material information relating to the registrant, including itsconsolidated subsidiaries, is made known to us by others within those entities,particularly during the period in which this report is being prepared;           (b) Designed such internal control over financial reporting, or causedsuch internal control over financial reporting to be designed under oursupervision, to provide reasonable assurance regarding the reliability offinancial reporting and the preparation of financial statements for externalpurposes in accordance with generally accepted accounting principles;           (c) Evaluated the effectiveness of the registrant’s disclosure controlsand procedures and presented in this report our conclusions about theeffectiveness of the disclosure controls and procedures, as of the end of theperiod covered by this report based on such evaluation; and           (d) Disclosed in this report any change in the registrant’s internalcontrol over financial reporting that occurred during the registrant’s mostrecent fiscal quarter (the registrant’s fourth fiscal quarter in the case of anannual report) that has materially affected, or is reasonably likely tomaterially affect, the registrant’s internal control over financialreporting; and           5. The registrant’s other certifying officer(s) and I have disclosed, based on our mostrecent evaluation of internal control over financial reporting, to the registrant’s auditors andthe audit committee of the registrant’s board of directors (or persons performing the equivalentfunctions):           (a) All significant deficiencies and materialweaknesses in the design or operation of internalcontrol over financial reporting which arereasonably likely to adversely affect theregistrant’s ability to record, process, summarizeand report financial information; and           (b) Any fraud, whether or not material, thatinvolves management or other employees who have asignificant role in the registrant’s internalcontrol over financial reporting.     /s/ David W. Sharp       David W. Sharp  *President and Chief Executive Officer*  Horizon Offshore, Inc.Date: November 1, 2007