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Boron-containing materials, and in particular boron nitride, have recently been identified as highly selective catalysts for the oxidative dehydrogenation of alkanes such as propane. To date, no mechanism exists that can explain both the unprecedented selectivity, the observed surface oxyfunctionalization, and the peculiar kinetic features of this reaction. We combine catalytic activity measurements with quantum chemical calculations to put forward a bold new hypothesis. We argue that the remarkable product distribution can be rationalized by a combination of surface-mediated formation of radicals over metastable sites, and their sequential propagation in the gas phase. Based on known radical propagation steps, we quantitatively describe the oxygen pressure-dependent relative formation of the main product propylene and by-product ethylene. Free radical intermediates most likely differentiate this catalytic system from less selective vanadium-based catalysts.