In many species that form socially monogamous pair bonds, a considerable proportion of the offspring is sired by extrapair males. This observation has remained a puzzle for evolutionary biologists: although mating outside the pair bond can obviously increase the offspring production of males, the benefits of such behavior to females are less clear, yet females are known to actively solicit extrapair copulations. For more than two decades adaptionist explanations have dominated the discussions, yet remain controversial, and genetic constraint arguments have been dismissed without much consideration. An intriguing but still untested hypothesis states that extrapair mating behavior by females may be affected by the same genetic variants (alleles) as extrapair mating behavior by males, such that the female behavior could evolve through indirect selection on the male behavior. Here we show that in the socially monogamous zebra finch, individual differences in extrapair mating behavior have a hereditary component. Intriguingly, this genetic basis is shared between the sexes, as shown by a strong genetic correlation between male and female measurements of extrapair mating behavior. Hence, positive selection on males to sire extrapair young will lead to increased extrapair mating by females as a correlated evolutionary response. This behavior leads to a fundamentally different view of female extrapair mating: it may exist even if females obtain no net benefit from it, simply because the corresponding alleles were positively selected in the male ancestors.