Efficient methods for storing and querying are critical for scaling high-order m-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily held in memory, while supporting queries needed in computing language model probabilities on-the-fly. We present several optimizations which improve query runtimes up to 2500x, despite only incurring a modest increase in construction time and memory usage. For large corpora and high Markov orders, our method is highly competitive with the state-of-the-art KenLM package. It imposes much lower memory requirements, often by orders of magnitude, and has runtimes that are either similar (for training) or comparable (for querying).