In this paper, we tackle the task of online video temporal grounding (OnVTG), which requires the model to locate events related to a given text query within a video stream. Unlike regular video temporal grounding, OnVTG requires the model to make predictions without observing future frames. As online videos are streaming inputs and can go on indefinitely, it is impractical and inefficient to store all historical inputs. The existing OnVTG models employ memory to store recent historical video frame features and predict scores indicating whether the current frame corresponds to the start or end time of the target event. However, these methods lack effective event modeling and cannot retain long-term historical information, leading to low performance. To tackle these challenges, we propose a hierarchical event memory for OnVTG. We propose an event-based OnVTG framework that makes predictions based on event proposals that model event-level information with various durations. To preserve historically valuable event information, we introduce a hierarchical event memory that retains historical events, allowing the model to access both recent and long-term information. To enable the real-time prediction, we further propose a future prediction branch that predicts whether the target event will occur shortly and further regresses the start time of the event. We achieve state-of-the-art performance on the TACoS, ActivityNet Captions, and MAD datasets. Code is available at https://github.com/minghangz/OnVTG.