Peer-to-peer (P2P) overlay networks are widely employed in distributed systems. The number of hops required by a node to locate an object is the fundamental search cost of a P2P network. Creating replicas can efficiently reduce the cost of object search, so how to deploy replicas to reduce the cost as much as possible is a critical problem of P2P networks. In the literature, most existing replica placement strategies arrange replicas at nodes near the one containing the considered object. In this paper, we formally demonstrate that for a complete Chord P2P network and many non-complete Chord ones, due to their deterministic structures, we can allocate replicas to nodes closest to the target in the identifier space to maximize the reduction in the total number of hops required by all nodes to reach a copy of the object during the search heading to the target node.