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In urban drainage systems (UDS), a proven method for reducing the combined sewer overflow (CSO) pollution is real-time control (RTC) based on model predictive control (MPC). MPC methodologies for RTC of UDSs in the literature rely on the computation of the optimal control strategies based on deterministic rain forecast. However, in reality, uncertainties exist in rainfall forecasts which affect severely accuracy of computing the optimal control strategies. Under this context, this work aims to focus on the uncertainty associated with the rainfall forecasting and its effects. One option is to use stochastic information about the rain events in the controller; in the case of using MPC methods, the class called stochastic MPC is available, including several approaches such as the chance-constrained MPC method. In this study, we apply stochastic MPC to the UDS using the chance-constrained method. Moreover, we also compare the operational behavior of both the classical MPC with perfect forecast and the chance-constrained MPC based on different stochastic scenarios of the rain forecast. The application and comparison have been based on simulations using a SWMM model of the Astlingen urban drainage benchmark network.