From crystal orbital calculations, benzene is found to chemisorb with nearly equal binding energy on a hollow site and on a bridge site of the Pt (111) face. The chemisorption is stronger and involves larger molecular distortions than on palladium and rhodium surfaces in agreement with experiment. On the hollow site, the benzene molecule undergoes a Kekulé distortion. On the bridge site found experimentally (with or without coadsorbed CO), the benzene molecule undergoes a local C2v distortion with long and short C-C bonds also in qualitative agreement with experiment. The favored azimuthal orientation of pure benzene coincides with that found experimentally only in the presence of CO. According to calculations, CO adsorption is found to weaken the benzene adsorption and reduce its metal-induced distortions but preserved the same orientation.