**Exhibit 31.1**
**CERTIFICATION**
I, William G. Hargett, certify that:
1.  I have reviewed this annual report on Form 10-K of The Houston Exploration Company; 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 included inthis 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 thisreport; 4.  The registrant’s other certifying officer 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 controlsand procedures to be designed under our supervision, to ensure that material informationrelating to the registrant, including its consolidated subsidiaries, is made known to usby others within those entities, particularly during the period in which this report isbeing prepared;  b)  Designed such internal control over financial reporting, or caused such internalcontrol over financial reporting to be designed under our supervision, to providereasonable assurance regarding the reliability of financial reporting and the preparationof financial statements for external purposes in accordance with generally acceptedaccounting principles;  c)  Evaluated the effectiveness of the registrant’s disclosure controls and proceduresand presented in this report our conclusions about the effectiveness of the disclosurecontrols and procedures, as of the end of the period covered by this report based on suchevaluation; and  d)  Disclosed in this report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of an annual report) that has materiallyaffected, or is reasonably likely to materially affect, the registrant’s internal controlover financial reporting; and
5.  The registrant’s other certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and theaudit committee of the registrant’s board of directors (or persons performing the equivalentfunctions):
 a)  All significant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely to adversely affectthe 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 whohave a significant role in the registrant’s internal control over financial reporting.        Date: February 22, 2005 /s/ William G. Hargett   William G. Hargett   Chairman, President and Chief Executive Officer