Chimpanzees are well known for their tool using abilities. Numerous studies have documented variability in tool use among chimpanzees and the role that social learning and other factors play in their development. There are also findings on hand use in both captive and wild chimpanzees; however, less understood are the potential roles of genetic and non-genetic mechanisms in determining individual differences in tool use skill and laterality. Here, we examined heritability in tool use skill and handedness for a probing task in a sample of 243 captive chimpanzees. Quantitative genetic analysis, based on the extant pedigrees, showed that overall both tool use skill and handedness were significantly heritable. Significant heritability in motor skill was evident in two genetically distinct populations of apes, and between two cohorts that received different early social rearing experiences. We further found that motor skill decreased with age and that males were more commonly left-handed than females. Collectively, these data suggest that though non-genetic factors do influence tool use performance and handedness in chimpanzees, genetic factors also play a significant role, as has been reported in humans.