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We report our attempts to locate the progenitor of the type Ic SN 2004gt inNGC 4038. We use high resolution HST ACS images of SN 2004gt and have comparedthem with deep pre-explosion HST WFPC2 F336W, F439W, F555W and F814W images. Weidentify the SN location on the pre-explosion frames with an accuracy of 5mas.We show that the progenitor is below the detection thresholds of all thepre-explosion images. These detection limits are used to place luminosity andmass limits on the progenitor, by comparing them with stellar evolution trackson the Hertzsprung-Russell diagram. The progenitor of SN 2004gt seems to berestricted to a low-luminosity high-temperature star, either a single WC starwith initial mass $>40M_{\odot}$ or a low mass star in a binary. Thepre-explosion data cannot distinguish between the two scenarios.Comment: ApJL accepted - 12 pages, 2 figures -minor changes due to referee's  comment

Luminosity and Mass Limits for the Progenitor of the Type Ic Supernova 2004gt in NGC 4038