Resolvability or recursive feasibility is an essential property for robust model predictive controllers. However, when an unbounded stochastic uncertainty is present, it is generally impossible to guarantee resolvability. We propose a new concept called probabilistic resolvability. A model-predictive control (MPC) algorithm is probabilistically resolvable if it has feasible solutions at future time steps with a certain probability, given a feasible solution at the current time. We propose a novel joint chance-constrained MPC algorithm that guarantees probabilistic resolvability. The proposed algorithm also guarantees the satisfaction of a joint chance-constraint, which specifies a lower bound on the probability of satisfying a set of state constraints over a finite horizon. Furthermore, with moderate conditions, the finite-horizon optimal control problem solved at each time step in the proposed algorithm is a convex optimization problem.