This Letter presents wide-field optical and near-IR (UBVRIHαK') images of the galaxy M74 that were taken between 0.6 and 8.3 yr before the discovery of the Type Ic supernova 2002ap. We have located the position of the supernova on these images with an accuracy of 0.3". We find no sign of a progenitor object on any of the images. The deepest of these images is the B-band exposure, which has a sensitivity limit corresponding to an absolute magnitude of MB<=-6.3. From our observed limits, we rule out as the progenitor all evolved states of single stars with initial masses greater than 20 Msolar unless the W-R phase has been entered. Two popular theories for the origin of Type Ic supernovae are the core collapse of massive stars when they are in the W-R phase or the core collapse of a massive star in an interacting binary that has had its envelope stripped through mass transfer. Our prediscovery images would be sensitive only to the most luminous ~30% of W-R stars, hence leaving a substantial fraction of typical W-R stars as viable progenitors. The energetics measured from modeling the initial light curve and spectral evolution of SN 2002ap suggest an explosion of a 5 Msolar C+O core. While W-R stars generally have measured final masses greater than this, the uncertainties associated with the explosion model, stellar evolutionary calculations, and mass measurements suggest we cannot definitively rule out a W-R star progenitor. The alternative scenario is that the progenitor was a star of initial mass ~20-25 Msolar that was part of an interacting binary and stripped of its hydrogen and helium envelope via mass transfer. We discuss future observations of the supernova environment that will provide further constraints on the nature of the progenitor star.