We introduce a lifelong language learning setup where a model needs to learn from a stream of text examples without any dataset identifier. We propose an episodic memory model that performs sparse experience replay and local adaptation to mitigate catastrophic forgetting in this setup. Experiments on text classification and question answering demonstrate the complementary benefits of sparse experience replay and local adaptation to allow the model to continuously learn from new datasets. We also show that the space complexity of the episodic memory module can be reduced significantly ( 50-90%) by randomly choosing which examples to store in memory with a minimal decrease in performance. We consider an episodic memory component as a crucial building block of general linguistic intelligence and see our model as a first step in that direction.