**Exhibit 31.1** **CERTIFICATION**     I, Scott A. Carmilani, certify that:     1. I have reviewed this Annual Report on    Form 10-K    of Allied World Assurance Company Holdings, Ltd;     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(s) 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))    and internal control over financial reporting (as defined in    Exchange Act Rules    13a-15(f)    and    15d-15(f))    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) Designed such internal control over financial    reporting, or caused such internal control over financial    reporting to be designed under our supervision, to provide    reasonable assurance regarding the reliability of financial    reporting and the preparation of financial statements for    external purposes in accordance with generally accepted    accounting principles;     (c) 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     (d) 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(s) 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. Dated:    February 29, 2008     /s/  Scott    A.    Carmilani                                                               Name:     Scott A. Carmilani    Title:       President and    Chief Executive Officer