We consider discrete-event systems (DES) involving the control of tasks with real-time constraints. When future event time information is limited, we propose a receding horizon (RH) controller in which only some future information is available within a time window. Analyzing sample paths obtained under this scheme and comparing them to optimal sample paths (obtained when all event times are known), we derive a number of attractive properties of the RH controller, including: the fact that it still guarantees all real-time constraints; there are segments of its sample path over which all controls are still optimal; the error relative to the optimal task departure times is decreasing under certain conditions. Simulation results are included to verify the properties of the controller and show that its performance can be near-optimal even if the RH window size is relatively small.