Many advances in Natural Language Processing have been based upon more expressive models for how inputs interact with the context in which they occur. Recurrent networks, which have enjoyed a modicum of success, still lack the generalization and systematicity ultimately required for modelling language. In this work, we propose an extension to the venerable Long Short-Term Memory in the form of mutual gating of the current input and the previous output. This mechanism affords the modelling of a richer space of interactions between inputs and their context. Equivalently, our model can be viewed as making the transition function given by the LSTM context-dependent. Experiments demonstrate markedly improved generalization on language modelling in the range of 3-4 perplexity points on Penn Treebank and Wikitext-2, and 0.01-0.05 bpc on four character-based datasets. We establish a new state of the art on all datasets with the exception of Enwik8, where we close a large gap between the LSTM and Transformer models.