This paper addresses a novel coordination problem for distributed agents in a discrete-event setting. We introduce and study a predicate coordination problem as the problem of distributed agents interacting and communicating between themselves to satisfy (the invariance of) a global predicate specifying an inter-agent constraint. We then develop an optimal coordination policy by which the agents can coordinate to satisfy the predicate constraint. To implement the optimal policy, we develop two on-line coordination strategies including one that can achieve significant savings in communication bandwidth.