We are interested in a new class of optimal control problems for Discrete Event Systems (DES). We adopt the formalism of supervisory control theory [12] and model the system as the marked language generated by a finite state machine (FSM). Our control problem follows the theory in [14] and is characterized by the presence of uncontrollable events, the notion of occurrence and control costs for events and a worst-case objective function. However, compared to the work in [14], we wish to take into account partial observability. Our solution approach consists of two steps. The first step is the derivation of an observer for the partially unobservable FSM, called a C-observer, which allows us to mask the underlying nondeterminis- m and to construct an approximation of the unobservable trajectory costs. We then define the performance measure on this observer rather than on the original FSM itself. In the second step, we use the algorithm presented in [14] to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system.