Play behaviour is common across mammals, but it is particularly frequent in primates. Several explanations for the occurrence of play have been proposed, both adaptive and nonadaptive. One popular explanation is that play supports the development of complex cognition and behavioural flexibility. This hypothesis is supported by a relationship between the relative size of several brain regions, including the neocortex and cerebellum, and the frequency of social play. However, a direct link with either behavioural flexibility or brain maturation has yet to be shown. Using a comparative data set of the frequency of social and nonsocial play across primates, I tested two predictions of this hypothesis: (1) that the frequency of play is associated with the amount of postnatal brain growth; and (2) that the frequency of play is associated with measures of behavioural flexibility. I found support for both predictions, and, notably, the results suggest that social and nonsocial play may contribute to different aspects of behavioural flexibility.