Many historical and contemporary theorists have proposed that population-level behavioral and brain asymmetries are unique to humans and evolved as a consequence of human-specific adaptations such as language, tool manufacture and use, and bipedalism. Recent studies in nonhuman animals, notably primates, have begun to challenge this view. Here, I summarize comparative data on neuroanatomical asymmetries in the planum temporale (PT) and inferior frontal gyrus (IFG) of humans and chimpanzees, regions considered the morphological equivalents to Broca's and Wernicke's areas. I also review evidence of population-level handedness in captive and wild chimpanzees. When similar methods and landmarks are used to define the PT and IFG, humans and chimpanzees show similar patterns of asymmetry in both cortical regions, though humans show more pronounced directional biases. Similarly, there is good evidence that chimpanzees show population-level handedness, though, again, the expression of handedness is less robust compared to humans. These results stand in contrast to reported claims of significant differences in the distribution of handedness in humans and chimpanzees, and I discuss some possible explanations for the discrepancies in the neuroanatomical and behavioral data.