The n-gram language model, which has its roots in statistical natural language processing, has been shown to successfully capture the repetitive and predictable regularities (“naturalness”) of source code, and help with tasks such as code suggestion, porting, and designing assistive coding devices. However, we show in this paper that this natural-language-based model fails to exploit a special property of source code: localness. We find that human-written programs are localized: they have useful local regularities that can be captured and exploited. We introduce a novel cache language model that consists of both an n-gram and an added “cache” component to exploit localness. We show empirically that the additional cache component greatly improves the n-gram approach by capturing the localness of software, as measured by both cross-entropy and suggestion accuracy. Our model’s suggestion accuracy is actually comparable to a state-of-the-art, semantically augmented language model; but it is simpler and easier to implement. Our cache language model requires nothing beyond lexicalization, and thus is applicable to all programming languages.