Since the BBS article in which Premack and Woodruff (1978) asked “Does the chimpanzee have a theory of mind?,” it has been repeatedly claimed that there is observational and experimental evidence that apes have mental state concepts, such as “want” and “know.” Unlike research on the development of theory of mind in childhood, however, no substantial progress has been made through this work with nonhuman primates. A survey of empirical studies of imitation, self-recognition, social relationships, deception, role-taking, and perspective-taking suggests that in every case where nonhuman primate behavior has been interpreted as a sign of theory of mind, it could instead have occurred by chance or as a product of nonmentalistic processes such as associative learning or inferences based on nonmental categories. Arguments to the effect that, in spite of this, the theory of mind hypothesis should be accepted because it is more parsimonious than alternatives or because it is supported by convergent evidence are not compelling. Such arguments are based on unsupportable assumptions about the role of parsimony in science and either ignore the requirement that convergent evidence proceed from independent assumptions, or fail to show that it supports the theory of mind hypothesis over nonmentalist alternatives. Progress in research on theory of mind requires experimental procedures that can distinguish the theory of mind hypothesis from nonmentalist alternatives. A procedure that may have this potential is proposed. It uses conditional discrimination training and transfer tests to determine whether chimpanzees have the concept “see.” Commentators are invited to identify flaws in the procedure and to suggest alternatives.