A context-aware language model uses location, user and/or domain metadata (context) to adapt its predictions. In neural language models, context information is typically represented as an embedding and it is given to the RNN as an additional input, which has been shown to be useful in many applications. We introduce a more powerful mechanism for using context to adapt an RNN by letting the context vector control a low-rank transformation of the recurrent layer weight matrix. Experiments show that allowing a greater fraction of the model parameters to be adjusted has benefits in terms of perplexity and classification for several different types of context.