Platinum supported on oxides is widely used in oxidation catalysis, including many important environmental and energy applications. Recent experiments have demonstrated that the active phase of Pt as well as several other transition-metal oxidation catalysts is not metallic but may be metal oxides. In order to better understand the effect of the particle size and chemical environment on Pt catalysts, we have performed density functional theory calculations to examine Pt nanoclusters in an oxidizing environment. We find that Pt nanoclusters exhibit size-dependent reactivity for CO and NO oxidation that is different from bulk Pt, and that the reactivity is also affected by the extent of the oxidation of the clusters. Interaction with oxide supports in turn modifies both the oxidation thermodynamics and the reactivity of the clusters. The results provide insight into the coupling among particle size, support, chemical environment, and reactivity and complement on-going experiments to explore the chemistry of supported metal nanoclusters.