X chromosome inactivation in female mammals results in dosage compensation of X-linked gene products between the sexes. In humans there is evidence that a substantial proportion of genes escape from silencing. We have carried out a large-scale analysis of gene expression in lymphoblastoid cell lines from four human populations to determine the extent to which escape from X chromosome inactivation disrupts dosage compensation. We conclude that dosage compensation is virtually complete. Overall expression from the X chromosome is only slightly higher in females and can largely be accounted for by elevated female expression of approximately 5% of X-linked genes. We suggest that the potential contribution of escape from X chromosome inactivation to phenotypic differences between the sexes is more limited than previously believed.