Traditional security mechanisms isolate resources from users who should not access them. We reflect the compositional nature of such security mechanisms back into the structure of LLMs to build a provably secure LLM; that we term SecureLLM. Other approaches to LLM safety attempt to protect against bad actors or bad outcomes, but can only do so to an extent making them inappropriate for sensitive data. SecureLLM blends access security with fine-tuning methods. Each data silo has associated with it a separate fine-tuning and a user has access only to the collection of fine-tunings that they have permission for. The model must then perform on compositional tasks at the intersection of those data silos with the combination of those individual fine-tunings. While applicable to any task like document QA or making API calls, in this work we concern ourselves with models that learn the layouts of new SQL databases to provide natural-language-to-SQL translation capabilities. Existing fine-tuning composition methods fail in this challenging environment, as they are not well-equipped for handling compositional tasks. Compositionality remains a challenge for LLMs. We contribute both a difficult new compositional natural-language-to-SQL translation task and a new perspective on LLM security that allows models to be deployed to secure environments today.