This paper extends the Diamond (1980) model with labor unions to study optimal income taxation and to analyze whether unions can be desirable for income redistribution. Unions bargain with firms over wages in each sector and firms unilaterally determine employment. Unions raise the efficiency costs of income redistribution, because unemployment benefits and income taxes raise wage demands and thereby generate involuntary unemployment. Optimal unemployment benefits and optimal income taxes are lower in unionized labor markets. We show that unions are socially desirable only if they represent (low-income) workers whose participation is subsidized on a net basis. By creating implicit taxes on work, unions alleviate the labor-market distortions caused by income taxation. Numerical simulations demonstrate that optimal taxes and transfers are much less redistributive in unionized labor markets than in competitive labor markets.