Production of the industrial chemical propylene oxide is energy-intensive and environmentally unfriendly. Catalysts based on bulk silver surfaces with direct propylene epoxidation by molecular oxygen have not resolved these problems because of substantial formation of carbon dioxide. We found that unpromoted, size-selected Ag₃ clusters and approximately 3.5-nanometer Ag nanoparticles on alumina supports can catalyze this reaction with only a negligible amount of carbon dioxide formation and with high activity at low temperatures. Density functional calculations show that, relative to extended silver surfaces, oxidized silver trimers are more active and selective for epoxidation because of the open-shell nature of their electronic structure. The results suggest that new architectures based on ultrasmall silver particles may provide highly efficient catalysts for propylene epoxidation.