(Abridged) We present a search for the progenitor star of the Type Ic Supernova 2002ap in deep, high quality pre-explosion observations taken with the Canada-France-Hawaii Telescope (CFHT). Aligning high-resolution Hubble Space Telescope (HST) observations of the supernova itself with the archival CFHT images allowed us to pinpoint the location of the progenitor site on the ground based observations. We find that a source visible in the B and R band pre-explosion images close to the position of the SN is (1) not coincident with the SN position within the uncertainties of our relative astrometry, and (2) is still visible ~ 4.7 yrs post-explosion in late-time observations taken with the William Herschel Telescope. We therefore conclude that it is not the progenitor of SN 2002ap. Comparing our luminosity limits with stellar models of single stars at appropriate metallicity (Z=0.008) we conclude that any single star progenitor must have experienced at least twice the standard mass loss rates during pre-Wolf-Rayet evolution, been initially > 30-40M(Sun) and exploded as a Wolf-Rayet star of final mass 10-12M(Sun). Alternatively an initially less massive progenitor may have evolved in an interacting binary system. We constrain any possible binary companion to a main sequence star of < 20M(Sun), a neutron star or a black hole. By combining the pre-explosion limits with the ejecta mass estimates and constraints from X-ray and radio observations we conclude that any binary interaction most likely occurred as Case B mass transfer, either with or without a subsequent common envelope evolution phase.
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