Using confocal fluorescence microscopy under ultrahigh vacuum conditions, we investigate the heterogeneous interactions between a perylene bisimide fluorophore and single crystalline Al2O3 (0001) at the single molecule level. We find that the dye molecules undergo reversible transitions to long-lived dark states, with bright and dark periods lasting from several hundred milliseconds to many tens of seconds. These periods are power-law distributed and point towards charge tunneling processes from the molecule to the substrate. The fluorescence intensity levels show a bimodal distribution, indicating different classes of adsorption sites on the sapphire surface. This study is aimed at obtaining a better understanding of interfacial structure and dynamics in order to address ultimately both the growth of organic semiconductor films on inorganic surfaces and the heterogeneous nature of charge transfer in excitonic solar cells.