With the high proportion of Distributed Generation (DG) connected to the grid, traditional deterministic reactive power optimization methods cannot deal with the double-sided uncertainties of DGs and load. This paper proposes a two-stage chance-constrained reactive power optimization method for an active distribution network. First, the power flow equation of the network is linearized and relaxed, and a two-stage reactive power optimization model based on a mixed integer second-order cone is established. In the first stage, discrete control devices such as the on-load tap changer and shunt capacitor are optimized. In the second stage, the uncertainties of DGs are considered to optimize the reactive power output of the DG. Then, a scenario reduction method is used to reduce the number of scenarios of the chance-constrained optimization method. Smulation results of a 95-bus system show that the proposed method can effectively eliminate the problem of security constraint violations, and achieve higher robustness with slightly increased network loss compared with the deterministic reactive power optimization method. This work is supported by the National Key Research and Development Program of China (No. 2017YFB0903705).