This paper explores the construction and contestation of moral distinctions as a dimension of contemporary structural inequality through a focus on the subjectivities constructed by young people who have experienced homelessness. Empirical material from two research projects shows that in young people's narratives of homelessness, material insecurity intertwines with the moral economies at work in neoliberal capitalist societies to construct homelessness as a state of moral disgrace, in which an ungovernable experience is experienced as a moral failure. When young people gain access to secure housing, the increasing stability and security of their lives is narrated in terms of a moral adherence to personal responsibility and disciplined conduct. Overall the paper describes an economy of worth organized around distinctions between order and chaos, self-governance and unruliness, morality and disgrace, which structures the experience of homelessness. As young people's position in relation to these moral ideals reflects the material conditions of their lives, their experiences demonstrate the way that moral hierarchies contribute to the existence and experience of structural inequalities in neoliberal capitalist societies.