Discovering frequent patterns over event sequences is an important data mining problem. Existing methods typically require multiple passes over the data, rendering them unsuitable for streaming contexts. We present the first streaming algorithm for mining frequent patterns over a window of recent events in the stream. We derive approximation guarantees for our algorithmin terms of: (i) the separation of frequent patterns fromthe infrequent ones, and (ii) the rate of change of streamcharacteristics.Our parameterization of the problem provides a new sweet spot in the tradeoff between making distributional assumptions over the stream and algorithmic efficiencies of mining. We illustrate how this yields significant benefits when mining practical streams from neuroscience and telecommunications logs.