Discovering frequent episodes over event sequences is an important data mining problem but existing methods are typically multi-pass, rendering them unsuitable for a streaming context. We present the first streaming algorithm for mining frequent episodes over a window of recent events in the stream. We derive approximation guarantees for our algorithm in terms of the separation frequent episodes exhibit from infrequent ones and the rate of change of stream characteristics. Our unique parameterization of the problem provides a new sweet spot in the tradeoff between making distributional assumptions over the stream and algorithmic efficiencies in mining. We illustrate how this yields significant benefits in mining practical streams from neuroscience and telecommunications logs.