This paper argues that localized price spikes should be a regular feature of competitive commodity markets. It develops a rational expectations model of physical arbitrage in which trade takes time, and shows that inventory management plays a crucial role in the way regional prices are determined. In equilibrium, arbitrageurs choose export quantities to ensure inventories in the importing center regularly fall to 0. They earn enough profits from high prices on these occasions to offset small losses at other times. An analysis of detailed data from Chicago and New York corn markets provides empirical support for the model.