We design and study a Contextual Memory Tree (CMT), a learning memory controller that inserts new memories into an experience store of unbounded size. It operates online and is designed to efficiently query for memories from that store, supporting logarithmic time insertion and retrieval operations. Hence CMT can be integrated into existing statistical learning algorithms as an augmented memory unit without substantially increasing training and inference computation. Furthermore CMT operates as a reduction to classification, allowing it to benefit from advances in representation or architecture. We demonstrate the efficacy of CMT by augmenting existing multi-class and multi-label classification algorithms with CMT and observe statistical improvement. We also test CMT learning on several image-captioning tasks to demonstrate that it performs computationally better than a simple nearest neighbors memory system while benefitting from reward learning.