In contrast to the widely studied problem of recognizing an action given a complete sequence, action anticipation aims to identify the action from only partially available videos. As such, it is therefore key to the success of computer vision applications requiring to react as early as possible, such as autonomous navigation. In this paper, we propose a new action anticipation method that achieves high prediction accuracy even in the presence of a very small percentage of a video sequence. To this end, we develop a multi-stage LSTM architecture that leverages context-aware and action-aware features, and introduce a novel loss function that encourages the model to predict the correct class as early as possible. Our experiments on standard benchmark datasets evidence the benefits of our approach; We outperform the state-of-the-art action anticipation methods for early prediction by a relative increase in accuracy of 22.0% on JHMDB-21, 14.0% on UT-Interaction and 49.9% on UCF-101.