The prevailing interpretation of constituent power is taken to be the extra-institutional capacity of a group, typically ‘the people’, to establish or revise the basic constitutional conditions of a state. Among many contemporary democratic theorists, this is understood as a collective capacity for innovation. This paper excavates an alternative perspective from constituent power’s genealogy. I argue that constituent power is not a creative material power, but is a type of political claim that shapes the collective rights, responsibilities and identity of ‘the people’. I do so by recovering Thomas Hobbes’s intervention into debates over constituent power among Scottish Presbyterians during the English Civil War. Though a materialist, Hobbes appreciated the centrality of the imagination to politics, and he argued that constituent power was one such phantasm of the mind. In Leviathan, he showed constituent power not to be a material power, but a world-making fiction that furnished political realities with ornamentation of the imagination, which might provide the beliefs and justifications to serve any number of political ends. More generally, the retrieval of a Hobbesian constituent power provides an important challenge to contemporary theories by demonstrating how partisan constructions of constituent power shape the political options available to groups.