We study how to improve predictive typing via per-user personalization of a pretrained large language model (LLM). We evaluate personalization in a time-ordered setting, using each user’s earlier messages for adaptation as we try to predict their next message. We compare: (1) personalization versus a non-personalized base model, (2) differing amounts of left context, (3) one-time adaptation versus making small periodic updates, and (4) full fine-tuning versus parameter-efficient fine-tuning. We find both static and personalized LLMs significantly outperform an n-gram language model. This includes when the n-gram was mixed with a user model learned via prediction by partial matching (PPM). Using long recent user-specific context provided the largest personalization gains: conditioning on up to 1024 previous characters reduced the base model’s perplexity by 18%. We found fine-tuning model weights provided only a small additional gain.