Age of Information (AoI) is an emerging concept to model information freshness from the perspective of destinations of information deliveries. Serving as a metric to characterize the data delivery timeliness, the peak age indicates the maximum value of the AoI prior to a data packet reception. In this paper, we present a distributed scheduling algorithm for peak age optimization in a wireless network where a number of sensor nodes attempt to deliver their sensed data to a data collector over a wireless channel. In particular, each sensor node accesses the channel for data delivery independently according to an adaptively tuned transmission probability. The beauty of our algorithm lies in that, even with neither centralized infrastructure nor coordinations among the sensor nodes, our algorithm asymptotically approximates the optimal solution by only a constant factor. We perform solid theoretical analysis and extensive simulations to verify the efficacy of our algorithm. To the best of our knowledge, it is the first fully distributed scheduling algorithm for AoI optimization in wireless networks.