Estimating origin–destination (OD) demand is essential for urban transport management and traffic control systems. With the ubiquity of smartphones, location based social networks (LBSN) data has emerged as a new rich data source with broad urban spatial and temporal coverage highly suitable for OD estimation. Its nature of confirmed trip purpose (activity) and activity chain host makes it more advantageous than other data (e.g., household travel surveys and traffic network detection). On the other hand, LBSN data is a more direct and accurate representation of demand patterns and can remove the significant burden of developing traffic models and estimating simulation-based objective functions. However, thus far, most LBSN-based estimation models only focus on static (day-level) OD estimation, making less use of those characteristics. To this end, this paper establishes a two-stage stochastic programming (TSSP) framework integrating the activity chains to model activity-level dynamic 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. Markov chain Monte Carlo (MCMC) sampling is used to generate plausible check-in scenarios. A generalized Benders decomposition (GBD) algorithm is presented to solve the two-stage stochastic programming model. We conduct the experiments on the case study of Tokyo, Japan, under the employment of the generalized least squares (GLS) estimator. The results show that algorithm convergence can be guaranteed within several iterations. The approach can provide satisfactory estimations of check-in patterns, zonal production and attraction, and OD flows. Furthermore, multiple objective function states are tested for evaluating the completeness of the proposed framework and exploring its potential for simplification and extension. Incorporating specific penalty terms into the objective function also provides a way to verify the reliability of the two-stage structure and validate the effectiveness of the model. Finally, we discuss the model enhancement from the perspectives of online OD estimation by integrating with LBSN simulations, network-wide OD extrapolation using appropriate scaling methods, and removing the user-side data requirement by leveraging activity chain modeling. The proposed framework provides a novel and effective approach to OD demand estimation using LBSN data.