This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity co-efficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t -> infinity; the model's variance converges to zero as t -> infinity. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effiective averaged Lyapunov exponents.