The question this chapter addresses is whether or not the human right to subsistence, which is widely internationally recognized, is underpinned by a fundamental human right, which has a peremptory moral force parallel to that of classic negative human rights such that the persistence of severe poverty should be classified as a human rights violation. While it is uncontroversial that torture or genocide, for example, constitute human rights violations, the claim that the persistence of severe poverty constitutes a human rights violation is much more controversial. The chapter argues that there is a fundamental moral human right to subsistence, and that the ongoing allowing and infliction of severe poverty constitutes a human rights violation that demands abolition. It also argues that the existing international practice of human rights fails to adequately recognize some of the duties not to violate this right, and some of the respects in which the right is being violated.