Landlords and tenants, on average, have opposite characteristics; but they display positive assortative matching within rental markets. In a nationwide data set containing administrative information on linked renter-occupiers and owners of investment properties in France, we document assortative matching by income level and composition, wealth, age, marital status and family structure, both across and within fine geographic segments. Consistent with a novel theory of rental housing assignment, the income correlation is only partially explained by observable characteristics such as location, size, or investment timing. This pattern has substantial implications for returns to wealth, and the incidence of housing market policies.