We offer a search-theoretic model of statistical discrimination, in which firms treat identical groups unequally based on their occupational choices. The model admits symmetric equilibria in which the group characteristic is ignored, but also asymmetric equilibria in which a group is statistically discriminated against, even when symmetric equilibria are unique. Moreover, a robust possibility is that symmetric equilibria become unstable when the group characteristic is introduced. Unlike most previous literature, our model can justify affirmative action since it eliminates asymmetric equilibria without distorting incentives.