We conduct a novel experimental test of the Coase conjecture based on subjects' privately known preferences for fairness. In an infinite horizon bargaining game, a proposer proposes a division of chips, until a responder accepts. When players are patient, the Coase conjecture predicts almost immediate agreement on equal monetary payoffs given any possibility a responder will not accept anything less. Behavior closely matches theory. In particular, when chips are worth more to proposers than responders, initial offers, minimum acceptable offers, responder payoffs, and efficiency are significantly larger in infinite horizon games than ultimatum games, and proposer payoffs are significantly smaller.