You can probably run it locally with llama.cpp using CPU only, but it will be slow. I have a couple year old laptop with a RTX 3060 and it runs pretty well split across the CPU and GPU.
I mean, hosting your own outside of OpenAI is mainly to avoid OpenAI accessing the data and using it for X, Y, and Z. I wouldn't roll my own if there weren't concerns about safety due to the cost and quality of the results.