Small clusters are known to possess reactivity not observed in their bulk analogues, which can make them attractive for catalysis. Their distinct catalytic properties are often hypothesized to result from the large fraction of under-coordinated surface atoms. Here, we show that size-preselected Pt(8-10) clusters stabilized on high-surface-area supports are 40-100 times more active for the oxidative dehydrogenation of propane than previously studied platinum and vanadia catalysts, while at the same time maintaining high selectivity towards formation of propylene over by-products. Quantum chemical calculations indicate that under-coordination of the Pt atoms in the clusters is responsible for the surprisingly high reactivity compared with extended surfaces. We anticipate that these results will form the basis for development of a new class of catalysts by providing a route to bond-specific chemistry, ranging from energy-efficient and environmentally friendly synthesis strategies to the replacement of petrochemical feedstocks by abundant small alkanes.