It has been proposed that human right handedness is determined by genetic factors associated with the emergence of language, whereas non-human primate handedness is determined by random, non-genetic factors. These different mechanisms account for differences in the distribution of handedness between human and non-human primates. Here we report evidence that genetic factors play a role in the determination of handedness in chimpanzees. We further report that differential rearing has no influence on the expression of handedness in related individuals. Contrary to many theories of the origin of handedness, these results indicate that genetic factors have a significant influence on handedness in chimpanzees.