Is it really possible to finetune LLMs to play chess?

I have an idea for my side project, I want to fine-tune an LLM to play chess and make sure it strictly makes legal moves and can compete with Chessbots and Human players. Is it possible to fine-tune an LLM and ensure it doesn't hallucinate? Another question I have is what kind of LLMs I should try to fine-tune. I am also interested in how I approach the data, should I train it on various openings and book methods or should I train it on various games played by players?

TLDR; trying to make a chess bot with LLMs, need help in approaching the problem