A fundamentally new psychology related to the ability to conceive of limited aspects of the self may have evolved in the ancestor of the great ape/human clade. Existing models of the evolution of primate intelligence do not provide an adequate explanation of the apparent restriction of this phenomenon. We propose that the capacity for self-conception evolved as a psychological mechanism enabling large-bodied, highly arboreal apes to cope with problems posed by the need to negotiate their way through a habitat that was fragile due to their body size. First, we briefly outline the case for believing that a new psychology related to self-conception evolved during the Miocene in the ancestor of the great ape/human clade. Next, we examine the existing models of the evolution of primate intelligence and assess their ability to account for the evolution of self-conception. Finally, we offer details of our alternative model, along with a series of predictions that can be derived from it.