Right–left regional cerebral differences are a feature of the human brain linked to functional abilities, aging, and neurodevelopmental and mental disorders. The role of genetic factors in structural asymmetry has been incompletely studied. We analyzed data from 515 individuals (130 monozygotic twin pairs, 97 dizygotic pairs, and 61 unpaired twins) from the Vietnam Era Twin Study of Aging to answer three questions about genetic determinants of brain structural asymmetry: First, does the magnitude of heritability differ for homologous regions in each hemisphere? Despite adequate power to detect regional differences, heritability estimates were not significantly larger in one hemisphere versus the other, except left > right inferior lateral ventricle heritability. Second, do different genetic factors influence left and right hemisphere size in homologous regions? Interhemispheric genetic correlations were high and significant; in only two subcortical regions (pallidum and accumbens) did the estimate statistically differ from 1.0. Thus, there was little evidence for different genetic influences on left and right hemisphere regions. Third, to what extent do genetic factors influence variability in left–right size differences? There was no evidence that variation in asymmetry (i.e., the size difference) of left and right homologous regions was genetically determined, except in pallidum and accumbens. Our findings suggest that genetic factors do not play a significant role in determining individual variation in the degree of regional cortical size asymmetries measured with MRI, although they may do so for volume of some subcortical structures. Despite varying interpretations of existing data, we view the present results as consistent with previous findings.