Recently, Fischer, Lynch and Paterson [3] proved that no completely asynchronous consensus protocol can tolerate even a single unannounced process death. We exhibit here a probabilistic solution for this problem, which guarantees that as long as a majority of the processes continues to operate, a decision will be made (Theorem 1). Our solution is completely asynchronous and is rather strong: As in [4], it is guaranteed to work with probability 1 even against an adversary scheduler who knows all about the system.