Time-dependent Origin-Destination (OD) demand flows are fundamental inputs for Dynamic Traffic Assignment (DTA) systems and real-time traffic management. This work introduces a novel state-space framework to estimate these demand flows in an online context. Specifically, we propose to explicitly include trip-chaining behavior within the state-space formulation, which is solved using the well-established Kalman Filtering technique. While existing works already consider structural information and recursive behavior within the online demand estimation problem, this information has been always considered at the OD level. In this study, we introduce this structural information by explicitly representing trip-chaining within the estimation framework. The advantage is twofold. First, all trips belonging to the same tour can be jointly calibrated. Second, given the estimation during a certain time interval, a prediction of the structural deviation over the whole day can be obtained without the need to run additional simulations. The effectiveness of the proposed methodology is demonstrated first on a toy network and then on a large real-world network. Results show that the model improves the prediction performance with respect to a conventional Kalman Filtering approach. We also show that, on the basis of the estimation of the morning commute, the model can be used to predict the evening commute without need of running additional simulations.