Large language models (LLMs) have become increasingly popular due to their ability to interact with unstructured content. As such, LLMs are now a key driver behind the automation of language processing systems, such as AI agents. Unfortunately, these advantages have come with a vulnerability to prompt injections, an attack where an adversary subverts the LLM's intended functionality with an injected task. Past approaches have proposed detectors and finetuning to provide robustness, but these techniques are vulnerable to adaptive attacks or cannot be used with state-of-the-art models. To this end we propose type-directed privilege separation for LLMs, a method that systematically prevents prompt injections. We restrict the ability of an LLM to interact with third-party data by converting untrusted content to a curated set of data types; unlike raw strings, each data type is limited in scope and content, eliminating the possibility for prompt injections. We evaluate our method across several case studies and find that designs leveraging our principles can systematically prevent prompt injection attacks while maintaining high utility.