This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set for constraint tightening with the help of the computation of the minimal robust positively invariant set, the chance constraints are guaranteed, assuming only the mean and covariance of the disturbance distribution are given. The resulting online optimization problem is a standard strictly quadratic programming, just like in conventional model predictive control with recursive feasibility and stability guarantees and is simple to implement. A numerical example is provided to illustrate the proposed method.