The concept of an evolutionary stable strategy (ESS) is a useful tool for studying the dynamics of natural selection. One of its limitations, however, is that it does not capture the notion of long-run stability when the system is subjected to stochastic effects. We define the concept of stability in a stochastic dynamical system, and show that it differs from both the traditional ESS and the concept of an attractor in a dynamical system. The stochastically stable set may be computed analytically using recent advances in potential theory.