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This paper describes a study in the evolution of distributed cooperative behavior, specifically leader election, through digital evolution and group selection. In digital evolution, a population of self-replicating computer programs exists in a user-defined computational environment and is subject to instruction-level mutations and natural selection. Group selection is the theory that the survival of the individual is linked to the survival of the group, thus encouraging cooperation. The results of experiments using the Avida digital evolution platform demonstrate that group selection can produce populations capable of electing a leader and, when that leader is terminated, electing a new leader. This result serves as an existence proof that group selection and digital evolution can produce complex cooperative behaviors, and therefore have promise in the design of robust distributed computing systems.