In this paper we extend the classical SIS epidemic model from a deterministic framework to a stochastic one, and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positive solution I(t) and establish conditions for extinction and persistence of I(t). We discuss the effects of the level of the stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real life diseases.