The social brain hypothesis, an explanation for the unusually large brains of primates, posits that the size of social group typical of a species is directly related to the volume of its neocortex. To test whether this hypothesis also applies at the within-species level, we applied the Cavalieri method of stereology in conjunction with point counting on magnetic resonance images to determine the volume of prefrontal cortex (PFC) subfields, including dorsal and orbital regions. Path analysis in a sample of 40 healthy adult humans revealed a significant linear relationship between orbital (but not dorsal) PFC volume and the size of subjects' social networks that was mediated by individual intentionality (mentalizing) competences. The results support the social brain hypothesis by indicating a relationship between PFC volume and social network size that applies within species, and, more importantly, indicates that the relationship is mediated by social cognitive skills.