This paper presents a method to design output feedback control for discrete-time linear systems, affected by bounded additive state, output disturbances, and subject to chance constraints on the state and hard constraints on the control input. This method relies on a so-called convex lifting which is a nonnegative, convex, piecewise affine function, equal to 0 over a given stochastic positively invariant set and strictly positive outside this set. Accordingly, it is shown that this function is strictly decreasing along the closed loop dynamics outside this invariant set and convergent to 0 as time tends to infinity. Consequently, the state is convergent to the given invariant set, while the method only requires solving a linear program at each sampling instant. (C) 2017 Elsevier Ltd. All rights reserved.