This document proposes a novel privacy enhancing routing algorithm called Optimal Privacy Enhancing Routing Algorithm (OPERA) for wireless networks. OPERA uses a statistical game-theoretic framework to optimize routing privacy given a utility function. It considers a global adversary that can observe transmissions across the entire network. OPERA formulates the privacy-utility tradeoff problem as a linear program that can be efficiently solved. Simulation results show that OPERA reduces the adversary's identification likelihood by up to half compared to random and greedy heuristics, and up to five times compared to a pattern matching scheme. OPERA also outperforms traditional information-theoretic approaches.