Across the animal kingdom, males tend to exhibit more behavioural and morphological variability than females, consistent with the 'greater male variability hypothesis'. This may reflect multiple mechanisms operating at different levels, including selective mechanisms that produce and maintain variation, extended male development, and X chromosome effects. Interestingly, human neuroanatomy shows greater male variability, but this pattern has not been demonstrated in any other species. To address this issue, we investigated sex-specific neuroanatomical variability in chimpanzees by examining relative and absolute surface areas of 23 cortical sulci across 226 individuals (135F/91M), using permutation tests of the male-to-female variance ratio of residuals from MCMC generalized linear mixed models controlling for relatedness. We used these models to estimate sulcal size heritability, simulations to assess the significance of heritability, and Pearson correlations to examine inter-sulcal correlations. Our results show that: (i) male brain structure is relatively more variable; (ii) sulcal surface areas are heritable and therefore potentially subject to selection; (iii) males exhibit lower heritability values, possibly reflecting longer development; and (iv) males exhibit stronger inter-sulcal correlations, providing indirect support for sex chromosome effects. These results provide evidence that greater male neuroanatomical variability extends beyond humans, and suggest both evolutionary and developmental explanations for this phenomenon.