The heritability of human personality is well-established. Recent research indicates that nonadditive genetic effects, such as dominance and epistasis, play a large role in personality variation. One possible explanation for the latter finding is that there has been recent selection on human personality. To test this possibility, we estimated additive and nonadditive genetic variance in personality and subjective well-being of zoo-housed orangutans. More than half of the genetic variance in these traits could be attributed to nonadditive genetic effects, modeled as dominance. Subjective well-being had genetic overlap with personality, though less so than has been found in humans or chimpanzees. Since a large portion of nonadditive genetic variance in personality is not unique to humans, the nonadditivity of human personality is not sufficient evidence for recent selection of personality in humans. Nonadditive genetic variance may be a general feature of the genetic structure of personality in primates and other animals.