Electronic communication allows interactions to take place over great distances. We build an agent-based model to explore whether networks that do not rely on geographic proximity can support cooperation as well as local interactions can. Adaptive agents play a four-move Prisoner's Dilemma game, where an agent's strategy specifies the probability of cooperating on the first move, and the probability of cooperating contingent on the partner's previous choice. After playing with four others, an agent adjusts its strategy so that more successful strategies are better represented in the succeeding round. The surprising result is that if the pattern of interactions is selected at random, but is persistent over time, cooperation emerges just as strongly as it does when interactions are geographically local. This has implications for both research on social dynamics, and for the prospects for building social capital in the modern age.