LLM are not doing well in chess. They do well when people play standard openings, but play against the LLM using an inexperienced player and the LLM will quickly start making illegal moves and be unable to play. There are many millions of pro chess games recorded on the internet, enough to cover all the openings and plenty of ways to go from there with some basic heuristics, but the more you diverge from those the more the LLM will break down since it doesn't understand the rules, it just memorized a lot of openings and some really primitive patterns to follow from there.