This paper constructs a stationary rational-expectations equilibrium in which an extraneous random variable, called animal spirits, causes fluctuations in unemployment. The model assumes costly matching in the labor market and a thin-market externality in the output market that makes the profitability of hiring depend positively on the number of firms hiring. The equilibrium does not rely on any effect of expected inflation on labor supply. It is also stable under learning; Bayesian updating induces convergence to the equilibrium with positive probability even if people start with no definite belief that animal spirits affect the profitability of hiring.