Although members of monozygotic twin pairs are identical in genome sequence, they may differ in patterns of gene expression. One early and irreversible process affecting gene expression, which can create differences within pairs of female monozygotic twins, is X inactivation — one twin can express mainly paternally-received genes on the X chromosome while the other twin expresses mainly maternally-received genes. It follows that non-identical X chromosome expression may cause female monozygotic twins to correlate less strongly than male monozygotic twins on complex behavioural traits affected by X-linked loci. We tested this hypothesis using data from around 4000 same-sex twin pairs on 9 social, behavioural and cognitive measures at ages 2, 3 and 4. Consistent with our hypothesis, monozygotic males were generally more similar than monozygotic females. Three of four significant differences were in traits showing higher correlations in males than females, and these traits — prosocial behaviour, peer problems, and verbal ability — have all been proposed previously in the literature as being influenced by genes on the X chromosome. Interestingly, dizygotic twins showed the reverse pattern of correlations for similar variables, which is also consistent with the X inactivation hypothesis; taken together, then, our monozygotic and dizygotic results suggest the presence of quantitative trait loci on the X chromosome.