Although there are only a few known examples of supported single-atom catalysts, they are unique because they bridge the gap between homogeneous and heterogeneous catalysis. Here, we report the CO oxidation activity of monodisperse single Pt atoms supported on an inert substrate, θ-alumina (Al2O3), in the presence of stoichiometric oxygen. Since CO oxidation on single Pt atoms cannot occur via a conventional Langmuir-Hinshelwood scheme (L-H scheme) which requires at least one Pt-Pt bond, we carried out a first-principles density functional theoretical study of a proposed pathway which is a variation on the conventional L-H scheme and inspired by the organometallic chemistry of platinum. We find that a single supported Pt atom prefers to bond to O2 over CO. CO then bonds with the oxygenated Pt atom and forms a carbonate which dissociates to liberate CO2, leaving an oxygen atom on Pt. Subsequent reaction with another CO molecule regenerates the single-atom catalyst. The energetics of the proposed mechanism suggests that the single Pt atoms will get covered with CO3 unless the temperature is raised to eliminate CO2. We find evidence for CO3 coverage at room temperature supporting the proposed mechanism in an in situ diffuse reflectance infrared study of CO adsorption on the catalyst's supported single atoms. Thus, our results clearly show that supported Pt single atoms are catalytically active and that this catalytic activity can occur without involving the substrate. Characterization by electron microscopy and X-ray absorption studies of the monodisperse Pt/θ-Al2O3 are also presented.