This paper examines two under-researched aspects of the public university, that of its relationship with the state, and with private universities. Chile, the case study here, possesses both public and private sectors of higher education, and has witnessed an intense debate over what it is to be a public university. The research focuses on a publicly documented government-sponsored debate. Three discourses are identified, turning on participants' views of the responsibilities of the state and the universities. The category of 'public' is seen to be fluid, attaching both to public-or state-owned-universities and to private universities. The conclusions are that, in a hybrid university system (of the Chilean kind), a university's publicness may be depicted as a profile of orientations and aspects and is no longer being confined solely to 'public universities': private universities are being seen as possessing public features. As an institution with a definite identity towards the state and society, what has been understood as the public university is in process of dissolution. It is, nevertheless, a situation that is opening new possibilities for what it is to be a public university both as institution and as idea.