Turns out, the primate best described by that old chestnut is none other than Homo sapiens. A new study in Science reports that, in a comparative study of human toddlers, chimpanzees, and orangutans, the human kids only exceeded their cousins in one area: what the authors call "social intelligence." Human toddlers were better able to guess the intentions of a researcher, and to repeat complex actions they'd seen demonstrated.
Humans Have Evolved Specialized Skills of Social Cognition: The Cultural Intelligence Hypothesis. Science, 317(5843): 1360-6.