This work is inspired by the daily operations of Hema supermarket, which is a recently established “new retail” model by Alibaba Group, China. In a Hema supermarket store, a single SKU may be presented with demand in the form of multiple channels. The challenge facing Hema is the question of how many units to stock in total between the warehouse and the store-front in advance of uncertain demand that arises in several consecutive time frames, each 30 minutes long. In this work, we provide the first distributionally robust optimization study in the setting of omnichannel inventory management, wherein we are to make a stocking decision robust to an adversary’s choice of coupling of available (marginal) demand distributions by channel and by time frame. The adversary’s coupling decision amounts to designing a random mathematical program with equilibrium constraints (MPEC). And we provide both a structural analysis of the adversary’s choice of couplingas well as an efficient procedure to find this coupling. In general, the overall distributionally robust stocking problem is non-concave. We provide sufficient conditions on the cost parameters under which this problem becomes concave, and hence tractable. Finally, we conduct experiments with Hema’s data. In these experiments, we compare and contrast the performance of our distributionally robust solution with the performance of a naive Newsvendor-like solution on various SKUs of varying sales volume and number of channels on a 5-hour time window from 2pm - 7pm on weekends. Numerical experiments show that the distributionally robust solutions generally outperform the stochastic Newsvendor-like solution. Furthermore, and interestingly, in all of our experiments, the distributionally robust inventory decision problems presented by the historical data provided by Hema are in fact concave.