CodexDB is an SQL processing engine whose internals can be customized via natural language instructions. CodexDB is based on OpenAI's GPT-3 Codex model which translates text into code. It is a framework on top of GPT-3 Codex that decomposes complex SQL queries into a series of simple processing steps, described in natural language. Processing steps are enriched with user-provided instructions and descriptions of database properties. Codex translates the resulting text into query processing code. An early prototype of CodexDB is able to generate correct code for a majority of queries of the WikiSQL benchmark and can be customized in various ways.