Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques is that code introduces new vocabulary at a far higher rate than natural language, as new identifier names proliferate. But traditional language models limit the vocabulary to a fixed set of common words. For code, this strong assumption has been shown to have a significant negative effect on predictive performance. But the open vocabulary version of the neural network language models for code have not been introduced in the literature. We present a new open-vocabulary neural language model for code that is not limited to a fixed vocabulary of identifier names. We employ a segmentation into subword units, subsequences of tokens chosen based on a compression criterion, following previous work in machine translation. Our network achieves best in class performance, outperforming even the state-of-the-art methods of Hellendoorn and Devanbu that are designed specifically to model code. Furthermore, we present a simple method for dynamically adapting the model to a new test project, resulting in increased performance. We showcase our methodology on code corpora in three different languages of over a billion tokens each, hundreds of times larger than in previous work. To our knowledge, this is the largest neural language model for code that has been reported.