Once considered a hallmark of human uniqueness, brain asymmetry has emerged as a feature shared with several other species, including chimpanzees, one of our closest living relatives. Most notable has been the discovery of asymmetries in homologues of cortical language areas in apes, particularly in the planum temporale (PT), considered a central node of the human language network. Several lines of evidence indicate a role for genetic mechanisms in the emergence of PT asymmetry; however, the genetic determinants of cerebral asymmetries have remained elusive. Studies in humans suggest that there is heritability of brain asymmetries of the PT, but this has not been explored to any extent in chimpanzees. Furthermore, the potential influence of non-genetic factors has raised questions about the reproducibility of earlier observations of PT asymmetry reported in chimpanzees. As such, the present study was aimed at examining both the heritability of phenotypic asymmetries in PT morphology, as well as their reproducibility. Using magnetic resonance imaging, we evaluated morphological asymmetries of PT surface area (mm2) and mean depth (mm) in captive chimpanzees (n = 291) derived from two genetically isolated populations. Our results confirm that chimpanzees exhibit a significant population-level leftward asymmetry for PT surface area, as well as significant heritability in the surface area and mean depth of the PT. These results conclusively demonstrate the existence of a leftward bias in PT asymmetry in chimpanzees and suggest that genetic mechanisms play a key role in the emergence of anatomical asymmetry in this region.