Even when global income redistribution is not feasible, market designers can seek to mitigate inequality within individual markets. If sellers are systematically poorer than buyers, for example, they will be willing to sell at relatively low prices. Yet a designer who cares about inequality might prefer to set higher prices precisely when sellers are poor-effectively, using the market as a redistributive tool. In this paper, we seek to understand how to design goods markets optimally in the presence of persistent inequality. Using a mechanism design approach, we find that redistribution through markets can indeed be optimal. When there is substantial inequality across sides of the market, the designer uses a tax-like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump-sum payments. When there is significant within-side inequality, meanwhile, the designer imposes price controls even though doing so induces rationing.