Chimpanzees at Mahale, Tanzania, show strong individual hand preferences when they use bimanual actions in processing the fruit of Saba florida and Citrus lemon. The direction of hand preference differs between the sexes: most males are left-handed, whereas most females are right-handed. Monkeys and apes are considered to lack “handedness,” in the sense of a population mode of left- or right-hand preference; they are normally ambidextrous. Indeed, strong individual preferences were previously seldom found in natural tasks. We propose that lateralization of manual actions becomes advantageous in bimanual tasks, which involve role differentiation between the hands and a need to combine power and precision. If the pattern of lateralization found here reflects the ancestral state, common to chimpanzees and humans, this may explain why, in modern humans, women tend more strongly to be right-handed than men, who include a larger minority of left-handers. Am J Phys Anthropol, 2003. © 2003 Wiley-Liss, Inc.