In this essay, Monaghan argues for an account of property possession as strict, numerical identity. According to this account, for an entity to possess a property is for that entity and that property to be numerically identical to each other. To defend this view, he argues against two views he call Externalism and Internalism about property possession. Monaghan argues that it is impossible for one entity to possess a second entity as a property. He provides replies to variety of objections one might raise against his account.