Energy efficient routing is a critical problem in multihop wireless networks due to the severe power constraint of wireless nodes. Despite its importance and many research efforts towards it, a distributed routing algorithm that maximizes network lifetime is still missing. To address this problem, we propose a novel utility-based nonlinear optimization formulation to the maximum lifetime routing problem. Based on this formulation, we further present a fully distributed, localized routing algorithm, which is proved to converge to the optimal point, where the network lifetime is maximized. Solid theoretical analysis and simulation results are presented to validate our solution.