Empirical evidence suggests that most urban systems experience a transition from a monocentric to a polycentric organization as they grow and expand. We propose here a stochastic, out-of-equilibrium model of the city, which explains the appearance of subcenters as an effect of traffic congestion. We show that congestion triggers the instability of the monocentric regime and that the number of subcenters and the total commuting distance within a city scale sublinearly with its population, predictions that are in agreement with data gathered for around 9000 U.S. cities between 1994 and 2010.