One unique part of Rousseau's Social Contract is his argument that a just society must have a specific constitutional arrangement of powers centred around what he calls the Sovereign and the Prince. This makes his philosophy different from other contractualists, such as Hobbes and Locke, who think that the principles of good government are compatible with any number of institutional structures. Rousseau's constitutional theory is thus significant in a way that has no parallel in Hobbes or Locke. More to the point, any problems that exist in his constitutional theory will have consequences for his political thought as a whole. This article argues that there is a contradiction at the center of Rousseau's theory of institutions that threatens the cogency of the Social Contract.