Human brain organization is built upon a more ancient adaptation, the large brain of simian primates: on average, monkeys and apes have brains twice as large as expected for mammals of their size, principally as a result of neocortical enlargement. Testing the adaptive benefit of this evolutionary specialization depends on finding an association between brain size and function in primates. However, most cognitive capacities have been assessed in only a restricted range of species under laboratory conditions. Deception of conspecifics in social circumstances is an exception, because a corpus of field data is available that encompasses all major lines of the primate radiation. We show that the use of deception within the primates is well predicted by the neocortical volume, when observer effort is controlled for; by contrast, neither the size of the rest of the brain nor the group size exert significant effects. These findings are consistent with the hypothesis that neocortical expansion has been driven by social challenges among the primates. Complex social manipulations such as deception are thought to be based upon rapid learning and extensive social knowledge; thus, learning in social contexts may be constrained by neocortical size.