The Coase theorem states that in public good problems, when there are no transaction costs, once property rights are well defined, the efficient outcome will always result. In particular, the assignment of property rights has, by itself, no efficiency implications; different allocations of property rights have merely distributive consequences. Under asymmetric information, however, the situation is completely different. The results of Rob (1989) and Mailath and Postlewaite (1990) indicate that, under asymmetric information, there is no way to overcome the "free-rider" problem. As the number of agents increases, the probablity of implementing the efficient outcome decreases to zero. By contrast, in this paper, we identify initial allocations of property rights that are compatible with the operation of an efficient mechanism. We present a mechanism that satisifies the conditions of incentive compatibility and individual rationality (with respect to this initial allocation of property rights) for the individuals and for the firm and that implements the efficient outcome in public good problems under asymmetric information. In this respect, we identify "efficient" property rights structures.