Lichess
A fully free, non-profit, open-source chess site — genuinely no ads, no premium tier, nothing gated.
Lichess is a registered non-profit and the entire codebase is open source — by its own account it's free, no ads, and stays that way on donations rather than a premium tier. In a category full of "free" products with a catch, this is one of the rare ones that isn't lying.