This paper shows that incomplete information can lead to self-fulfilling business cycles. This is demonstrated in a standard dynamic general equilibrium model of monopolistic competition à la Dixit-Stiglitz. In the absence of fundamental shocks, the model has a unique certainty (fundamental) equilibrium. But there are also multiple stochastic (sunspots) equilibria that are not mere randomizations over fundamental equilibria. Thus, sunspots can exist in infinite-horizon models with a unique saddle-path steady state. In contrast to the indeterminacy literature following Benhabib and Farmer (1994), sunspots are robust to parameters associated with production technologies and preferences.