A major research challenge in multi-agent systems is the problem of partitioning a set of agents into mutually disjoint coalitions, such that the overall performance of the system is optimized. This problem is difficult because the search space is very large: the number of possible coalition structures increases exponentially with the number of agents. Although several algorithms have been proposed to tackle this Coalition Structure Generation (CSG) problem, all of them suffer from being inherently centralized, which leads to the existence of a performance bottleneck and a single point of failure. In this paper, we develop the first decentralized algorithm for solving the CSG problem optimally. In our algorithm, the necessary calculations are distributed among the agents, instead of being carried out centrally by a single agent (as is the case in all the available algorithms in the literature). In this way, the search can be carried out in a much faster and more robust way, and the agents can share the burden of the calculations. The algorithm combines, and improves upon, techniques from two existing algorithms in the literature, namely DCVC [5] and IP [9], and applies novel techniques for filtering the input and reducing the inter-agent communication load.