When an model predictive controller (MPC) is subject to unbounded uncertainty, it is generally impossible to guarantee resolvability or recursive feasibility. In our previous work we developed an open-loop chance-constrained model predictive control (CCMPC) algorithm that is probabilistically resolvable [1], meaning that, given a feasible solution at the current time, the controller is guaranteed to find feasible solutions at future time steps with a certain probability. However, the controller is known to be overly conservative. In this paper we address this issue by extending this approach to a closed-loop CCMPC. We first develop a general closed-loop CCMPC framework building upon the affine disturbance feedback approach, and prove that the proposed closed-loop CCMPC is probabilistically resolvable. We also present two implementations of the proposed closed-loop CCMPC, whose finite-horizon optimal control problem solved at each time step is a convex optimization problem. We empirically demonstrate that the proposed closed-loop CCMPCs are significantly less conservative than the existing open-loop CCMPC.