We analyze the role of demand uncertainty in markets of fixed size, in which firms take long-run capacity decisions prior to competing in prices. We characterize the set of subgame perfect Nash equilibria under various assumptions regarding the nature and timing of demand uncertainty. In order to prove equilibrium existence, we identify a sufficient condition for the capacity choice game to be submodular. This condition resembles the standard downward-sloping marginal revenue condition used in Cournot games. A robust conclusion of the analysis is that equilibrium capacity choices are asymmetric, even when firms are ex-ante identical. Concerning the equivalence between the capacity-price game and the Cournot game, we find that with inelastic demands, the equilibria of the former belong to the equilibrium set of the latter. However, as compared to the Cournot game, the capacity-price game leads to lower prices and generates price dispersion.