Estimating origin-destination (OD) demand is indispensable for urban transport management and traffic control systems. While the existing estimation methods rely on data sources like household travel surveys and traffic network detection, they incur very high costs and are still either less frequent or low in coverage density triggering lower observability and indeterminacy issues for OD estimation. With ubiquity of smartphones, Location based social networks (LSBN) data has emerged as a new rich data source with broad urban spatial and temporal coverage highly suitable for OD estimation. However, thus far, most LSBN-based estimation models only focus on static (day-level) OD estimation. This paper establishes a two-stage stochastic programming (TSSP) framework integrating the activity chains to model activity-level mobility flows using LBSN data. The first stage model aims to minimize the errors introduced by the inter-zone OD flows alongside the expected errors of the check-in patterns. The second stage model attempts to minimize the errors produced by the considered check-in pattern scenarios. A generalized Benders decomposition algorithm is presented to solve the two-stage stochastic programming model. We conduct the experiments employing generalized least squares (GLS) estimator on the case study of Tokyo city. The results depict that the algorithm convergence can be guaranteed within several steps. The algorithm shows satisfactory performance in check-in pattern estimation, OD flows estimation, and activity share estimation. Further, the implementation of the model in practical applications is also specifically discussed.