Abstract: In his pioneering work on transaction costs, Ronald Coase presupposed a picture of property as a bundle of government-prescribed use rights. This picture is not only not essential to what Coase was trying to do, but its limitations emerge when we apply Coase’s central insights to analyze the structure of property itself. This leads to what we term the Coase Corollary: in a world of zero transaction costs the nature of property does not matter to allocative efficiency. But as with the Coase Theorem itself, the real point is the implication for a positive transaction cost world: we need to subject the notion of property to a comparative institutional analysis. Because transaction costs are positive, it is no accident that property is defined in terms of things as a starting point, that uses are grouped under exclusion rights, and that in rem rights are widely employed: these features of property receive a transaction cost explanation. Simple lumpy packages of property rights motivated by transaction costs form an important baseline that furnishes presumptive answers to bilateral use conflicts. A more thoroughly Coasean approach points back to a picture of property more like the traditional one furnished by the law.