Modern data center networks often adopt multipath topologies for greater bisection bandwidth and better fault tolerance. However, traditional distributed routing algorithms make routing decisions based on only packet destinations, and cannot readily utilize the multipath feature. In this paper, we study distributed multipath routing for data center networks. First, to capture the time varying and non-deterministic nature of data center network traffic, we present a stochastic traffic model based on the log normal distribution. Then, we formulate the stochastic load-balanced multipath routing problem, and prove that it is NP hard for typical data center network topologies, including the fat tree, VL2, DCell, and BCube. Next, we propose our distributed multipath routing algorithm, which balances traffic among multiple links by minimizing the probability of each link to face congestion. Finally, we implement the proposed algorithm in the NS2 simulator, and provide simulation results to demonstrate the effectiveness of our design.