Several recently emerged Internet services make use of application-level or overlay networks. Examples of such services include overlay multicast, structured peer-to-peer lookup services, and peer-to-peer file sharing. Many of these services could benefit from enabling participating end hosts to estimate their relative network locations within the overlay. In this paper, we present PCoord, a peer-to-peer network coordinate system for overlay topology discovery and distance prediction. The goal of PCoord is to allow participating peer nodes in an overlay network to collaboratively construct an accurate geometric model of the overlay network topology in a completely decentralized peer-to-peer fashion. We evaluate the PCoord approach through extensive simulations using both real network measurements and simulated topologies. Our results indicate that the constructed geometric model can give accurate pair-wise distance prediction and nearest neighbor discovery. In particular, using a simulated overlay network consisting of over 3,400 peer nodes, our results indicate that over 90% of the peers can predict their closest peers by probing only a small fraction of the global peer population.