People today typically use multiple online social networks (Facebook, Twitter, Google+, LinkedIn, etc.). Each online network represents a subset of their "real" ego-networks. An interesting and challenging problem is to reconcile these online networks, that is, to identify all the accounts belonging to the same individual. Besides providing a richer understanding of social dynamics, the problem has a number of practical applications. At first sight, this problem appears algorithmically challenging. Fortunately, a small fraction of individuals explicitly link their accounts across multiple networks; our work leverages these connections to identify a very large fraction of the network. Our main contributions are to mathematically formalize the problem for the first time, and to design a simple, local, and efficient parallel algorithm to solve it. We are able to prove strong theoretical guarantees on the algorithm's performance on well-established network models (Random Graphs, Preferential Attachment). We also experimentally confirm the effectiveness of the algorithm on synthetic and real social network data sets.