The estimation of genetic effects from twin studies usually relies upon the equal environment assumption — that monozygous (MZ) and dizygous (DZ) twin pairs experience equal similarity of their environments from prenatal experiences through adulthood. However, the sharing of a chorion may make a subset of identical twins more similar, or in some cases, more different, than twins that do not share a chorion. Recent studies suggest monochorionic MZ twins resemble one another more than dichorionic MZ twins in cognitive abilities, personality, and risk for psychiatric disorder. To the extent that prenatal environment affects these characteristics, the traditional twin method will yield biased estimates of genetic and environmental influences. We develop models for quantifying this bias and estimating the influence of chorion type on estimates of heritability.