The catalytic oxidation of carbon monoxide (CO) on a platinum (111) surface was studied by scanning tunneling microscopy. The adsorbed oxygen atoms and CO molecules were imaged with atomic resolution, and their reactions to carbon dioxide (CO2) were monitored as functions of time. The results allowed the formulation of a rate law that takes the distribution of the reactants in separate domains into account. From temperature-dependent measurements, the kinetic parameters were obtained. Their values agree well with data from macroscopic measurements. In this way, a kinetic description of a chemical reaction was achieved that is based solely on the statistics of the underlying atomic processes.