We analyze race discrimination in labor markets in which wage offers are posted. If employers with job vacancies receive multiple applicants, they choose the most qualified but may choose arbitrarily among equally qualified applicants. In the model, firms post wages, workers choose where to apply, and firms decide which workers to hire. Labor-market frictions greatly amplify racial disparities, so mild discriminatory tastes or small productivity differences can produce large wage differentials between the races. Compared with the nondiscriminatory equilibrium, the discriminatory equilibrium features lower net output, lower wages for both white and black workers and greater profits for firms.