In this paper we propose an output-feedback Model Predictive Control (MPC) algorithm for linear discrete-time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints. In case the noise distribution is unknown, the probabilistic constraints on the input and state variables are reformulated by means of the Chebyshev-Cantelli inequality. The recursive feasibility is guaranteed, the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions, and the implementation issues are thoroughly addressed. Two examples are discussed in detail, with the aim of providing an insight into the performance achievable by the proposed control scheme. (C) 2015 Elsevier Ltd. All rights reserved.