This paper studies the Nash equilibria of Hotelling’s pure location model (in which the space of location is a line segment and there is no price variable). It is shown that there is always a symmetric equilibrium in mixed strategies with certain properties, and that as the number of firms increases, the limiting equilibrium mixed strategy of each firm is equal to the distribution function of consumers on the line segment. For the case in which there are three firms and the distribution of consumers is uniform, a detailed analysis of the asymmetric equilibria is given.