An important problem in distributed systems is observation of global properties of distributed computations. What makes this problem difficult is that events in the computation can be concurrent, i.e. the relation between events forms a partial order, not a total order. One of the fundamental parameters of a partial order is the width, which corresponds to the maximum number of mutually incomparable elements. For example, a process-time diagram that shows this partial order decomposition in minimum number of chains can be very useful in monitoring or debugging such computations. In this paper, we present an incremental algorithm to compute the optimal chain partition. We compare our algorithm with existing chain reduction algorithms. From a practical point of view, performance evaluation shows that our approach achieves up to 90% run-time improvement over the previously known algorithms.