Density functional theory is used to compute electronic and thermodynamic interactions between atomic and molecular oxygen and small Pt, clusters (n = 2-6). Binding energies, vibrational frequencies, and charge distributions are reported. Two states are identified for the adsorption of molecular oxygen: the superoxo species (O-2(delta-)) and the peroxo species (O-2(2 delta-)) formed by charge transfer from the metal cluster to the O-2 molecule. An analysis of the adsorbed O-2 dissociation on Pt clusters illustrates the dependence of the activation barrier for dissociation on the metal cluster size.