Tunneling electrons from the tip of a scanning tunneling microscope were used to induce and monitor the reversible rotation of single molecules of molecular oxygen among three equivalent orientations on the platinum(111) surface. Detailed studies of the rotation rates indicate a crossover from a single-electron process to a multielectron process below a threshold tunneling voltage. Values for the energy barrier to rotation and the vibrational relaxation rate of the molecule were obtained by comparing the experimental data with a theoretical model. The ability to induce the controlled motion of single molecules enhances our understanding of basic chemical processes on surfaces and may lead to useful single-molecule devices.