While several techniques for detecting trace-level anomalies in event logs in offline settings have appeared recently in the literature, such techniques are currently lacking for online settings. Event log anomaly detection in online settings can be crucial for discovering anomalies in process execution as soon as they occur and, consequently, allowing to promptly take early corrective actions. This paper describes a novel approach to event log anomaly detection on event streams that uses statistical leverage. Leverage has been used extensively in statistics to develop measures to identify outliers and it has been adapted in this paper to the specific scenario of event stream data. The proposed approach has been evaluated on both artificial and real event streams.