The agents in multiagent systems can coordinate their actions and handle tasks jointly by forming coalitions. One of the important steps in this process is the fair division of payoff generated from such a joint effort among all coalition members. The nucleolus is widely recognized as a fair way of distributing the revenue in a coalition. While we have efficient algorithms for computing the nucleolus using linear programming based techniques, we believe that such approaches are infeasible in multiagent settings where the loci of decision making is distributed among all agents in the system, and there is no central agent that can aggregate all data and compute for all agents. Towards this end, in this paper we present a distributed algorithm that computes the nucleolus-stable payoff division for any multiagent system modeled as a characteristic form game. We empirically show that our algorithm has many desirable properties - it searches only a small fraction of the solution space, evenly distributes the computational load among all agents, and executes reasonably quickly for this hard problem.