Among nonhuman primates, chimpanzees are well known for their sophistication and diversity of tool use in both captivity and the wild. The evolution of tool manufacture and use has been proposed as a driving mechanism for the development of increasing brain size, complex cognition and motor skills, as well as the population-level handedness observed in modern humans. Notwithstanding, our understanding of the neurological correlates of tool use in chimpanzees and other primates remains poorly understood. Here, we assessed the hand preference and performance skill of chimpanzees on a tool use task and correlated these data with measures of neuroanatomical asymmetries in the inferior frontal gyrus (IFG) and the pli-de-passage fronto-parietal moyen (PPFM). The IFG is the homolog to Broca's area in the chimpanzee brain and the PPFM is a buried gyrus that connects the pre- and post-central gyri and corresponds to the motor-hand area of the precentral gyrus. We found that chimpanzees that performed the task better with their right compared to left hand showed greater leftward asymmetries in the IFG and PPFM. This association between hand performance and PPFM asymmetry was particularly robust for right-handed individuals. Based on these findings, we propose that the evolution of tool use was associated with increased left hemisphere specialization for motor skill. We further suggest that lateralization in motor planning, rather than hand preference per se, was selected for with increasing tool manufacture and use in Hominid evolution.