A resilience-oriented service restoration method using microgrids to restore critical load after natural disasters is proposed in this paper. Considering the scarcity of power generation resources, the concept of continuous operating time (COT) is introduced to determine the availability of microgrids for critical load restoration and to assess the service time. Uncertainties induced by intermittent energy sources and load are also taken into account. The critical load restoration problem is modeled as a chance-constrained stochastic program. A Markov chain-based operation model is designed to describe the stochastic energy variations within microgrids, based on which the COT is assessed. A two-stage heuristic is developed for the critical load restoration problem. First, a strategy table containing the information of all feasible restoration paths is established. Then the critical load restoration strategy is obtained by solving a linear integer program. Numerical simulations are performed on the IEEE 123-node feeder system under several scenarios to demonstrate the effectiveness of the proposed method. The impacts of fault locations, available generation resources, and load priority on the restoration strategy are discussed.