This paper sheds light on a recent empirical controversy about the effect of competition on price discrimination in airline markets (Borenstein and Rose (1994), Gerardi and Shapiro, (2009)). We introduce individual demand uncertainty into Hotellings model of horizontal product differentiation and show that in equilibrium, firms offer advance purchase discounts. Consumers tradeoff an early (uninformed) purchase at a low price against a late (informed) purchase at a high price. Relative to a (multi-product) monopolist, competing firms offer larger discounts, leading to an intertemporal distribution of sales that is more skewed towards low prices. We show that whether competition has a positive or a negative effect on the Gini coefficient of price dispersion depends on the degree of product differentiation and the level of demand uncertainty.