We study the design of child care subsidies in an optimal welfare problem with heterogeneous private market productivities. The optimal subsidy schedule is qualitatively similar to the existing US scheme. Efficiency mandates a subsidy on formal child care costs, with higher subsidies paid to lower income earners and a kink as a function of child care expenditure. Marginal labor income tax rates are set lower than the labor wedges, with the potential to generate negative marginal tax rates. We calibrate our simple model to features of the US labor market and focus on single mothers with children aged below 6. The optimal program provides stronger participation but milder intensive margin incentives for low-income earners with subsidy rates starting very high and decreasing with income more steeply than those in the United States. (author abstract)