I think an inherent issues is always going to be the existence of chess engines.

Sure, some sites claim they have ways to detect these engines, and ban players. But then it comes down to how do you ever know for sure that the site is actually banning cheaters or just banning people who win too frequently, and ensuring someone on the inside wins?

You might find a place to play for BTC, as others have listed... but you can never know if it is going to be fair at all.