9,10-Dithioanthracene adsorbed on Cu(111) diffuses exclusively along the high-symmetry axis of the molecule-substrate system. Further reduction of the symmetry of the system by asymmetric methylation does not reduce the symmetry of the motion although it has a substantial. effect on the diffusion rate (100-fold reduction) and renders the diffusion barrier asymmetric. This is in contrast to the behavior expected of a classical particle, and it provides a direct single-molecule-scale vista on the validity of The Principle of Microscopic Reversibility first formulated by Tolman in 1924, which despite its fundamental role has attracted little visualization.