Do judges have an obligation to apply the law of the legal system to which their courts belong? It can seem obvious that they do. But even the qualified proposition that judges in a legitimate legal system, i.e. one whose laws enjoy legitimate authority, have an obligation to apply the laws of that system is in fact far from simple to justify. The goal of this paper is to flesh out in some detail what such an obligation consists in – and thus what it is that one is trying to justify –, and to argue for a positive proposal as to how it could be justified. The proposal, which grounds judicial obligation on the value of the rule of law, has implications for our understanding of the nature of political legitimacy: that is, for our understanding of what is involved in establishing that some legally constituted political institution (or conglomerate of political institutions, such as those of a modern territorial state) is justified in its activities (including but not limited to coercive activities) and claims (including but not limited to the claim to possessing practical authority).