This paper presents a scalable leader election protocol for large process groups with a weak membership requirement. The underlying network is assumed to be unreliable but characterized by probabilistic failure rates of processes and message deliveries. The protocol trades correctness for scale, that is, it provides very good probabilistic guarantees on correct termination in the sense of the classical specification of the election problem, and of generating a constant number of messages, both independent of group size. After formally specifying the probabilistic properties, we describe the protocol in detail. Our subsequent mathematical analysis provides probabilistic bounds on the complexity of the protocol. Finally, the results of simulation show that the performance of the protocol is satisfactory.