We report deep imaging observations of the young, nearby star AB Pic, a member of the large Tucana-Horologium association. We have detected a faint, red source 5.5'' South of the star with JHK colors compatible with that of a young substellar L dwarf. Follow-up observations at two additional epochs confirm, with a confidence level of 4.7σ, that the faint red object is a companion to AB Pic rather than it being a stationary background object. A low resolution K-band spectrum indicates an early-L spectral type for the companion. Finally, evolutionary model predictions based on the JHK photometry of AB Pic b indicate a mass of 13 to 14 MJup if its age is ~30 Myr. Is AB Pic b a massive planet or a minimum mass brown dwarf?