This article attempts to answer two basic questions. First, can body parts be the subject of property rights? This requires us to start with a definition of property rights, and this is set out in the first section. In the second section, it will be argued that rights in relation to body parts can come within this definition of property rights. However, as explained in the third section, the fact that body parts can be the subject of property rights does not mean that they should. To answer the question of whether body parts should be the subject of property rights we need to consider policy arguments. This article will develop an argument in favour of the recognition of property rights in body parts which focuses on the notion of scarcity of resources.