We propose a new generative language model for sentences that first samples a prototype sentence from the training corpus and then edits it into a new sentence. Compared to traditional language models that generate from scratch either left-to-right or by first sampling a latent sentence vector, our prototype-then-edit model improves perplexity on language modeling and generates higher quality outputs according to human evaluation. Furthermore, the model gives rise to a latent edit vector that captures interpretable semantics such as sentence similarity and sentence-level analogies.