Weak fairness guarantees that continuously enabled actions are executed infinitely often. Strong fairness, on the other hand, guarantees that actions that are enabled infinitely often (but not necessarily continuously) are executed infinitely often. In this paper, we present a distributed algorithm for scheduling actions for execution. Assuming weak fairness for the execution of this algorithm, the schedule it provides is strongly fair. Furthermore, this algorithm is maximal in that it is capable of generating any strongly fair schedule. This algorithm is the first strongly-fair scheduling algorithm that is both distributed and maximal.