We are often asked whether some apes are smarter than others. Here we used two individual-based datasets on cognitive abilities to answer this question and to elucidate the structure of individual differences. We identified some individuals who consistently scored well across multiple tasks, and even one individual who could be classified as exceptional when compared with her conspecifics. However, we found no general intelligence factor. Instead, we detected some clusters of certain abilities, including inferences, learning and perhaps a tool-use and quantities cluster. Thus, apes in general and chimpanzees in particular present a pattern characterized by the existence of some smart animals but no evidence of a general intelligence factor. This conclusion contrasts with previous studies that have found evidence of a g factor in primates. However, those studies have used group-based as opposed to the individual-based data used here, which means that the two sets of analyses are not directly comparable. We advocate an approach based on testing multiple individuals (of multiple species) on multiple tasks that capture cognitive, motivational and temperament factors affecting performance. One of the advantages of this approach is that it may contribute to reconcile the general and domain-specific views on primate intelligence.