This paper analyses a duopolistic price setting game in which firms have loyal consumer segments, but cannot distinguish them from price sensitive consumers. We adapt a variant of Varian's [1980] simultaneous price setting game to analyse price leader equilibria. The properties of the price leader equilibria with an exogenously specified leader motivate the construction of a game of timing in which the firm with the larger segment of loyal consumers becomes an endogenous price leader. This demonstrates that consumer loyalty may play an important role in establishing the existence and identity of a price leader.