The catalytic activity of gold depends on particle size, with the reactivity increasing as the particle diameter decreases. However, investigations into behaviour in the subnanometre regime (where gold exists as small clusters of a few atoms) began only recently with advances in synthesis and characterization techniques. Here we report an easy method to prepare isolated gold atoms supported on functionalized carbon nanotubes and their performance in the oxidation of thiophenol with O2. We show that single gold atoms are not active, but they aggregate under reaction conditions into gold clusters of low atomicity that exhibit a catalytic activity comparable to that of sulfhydryl oxidase enzymes. When clusters grow into larger nanoparticles, catalyst activity drops to zero. Theoretical calculations show that gold clusters are able to activate thiophenol and O2 simultaneously, and larger nanoparticles are passivated by strongly adsorbed thiolates. The combination of both reactants activation and facile product desorption makes gold clusters excellent catalysts.