In this article I propose a cosmopolitan approach to animal rights based upon Kant's right of universal hospitality. Many approaches to animal rights buttress their arguments by finding similarities between humans and non-human animals; in this way they represent or resemble ethics of partiality. In this article I propose an approach to animal rights that initially rejects similarity approaches and is instead based upon the adoption of a cosmopolitan mindset acknowledging and respecting difference. Furthermore, and in agreement with Martha Nussbaum, and Sue Donaldson and Will Kymlicka, I endorse the view that theories of animal rights need to be theories of justice and include a political component. Contra Donaldson and Kymlicka, however, I argue that the starting point for analysis of political theories of animal rights should be at the global rather than national level. Taking animals as strangers, I propose adopting a Kantian cosmopolitan mindset and ethic of universal hospitality towards them. I address how a ius cosmopoliticum that is hospitable to the interests of non-human animals can govern interactions with animals on fair terms, and I respond to concerns that cosmopolitanism cannot accommodate non-human animals because it is a democratic ideal, is grounded in logocentrism or rests upon ownership of territory by humans.