C64 Chess Project (C64hess) by Chessforeva (2015) is a chess puzzle game where you try to achieve checkmate in 1, 2 or 3 moves.

Chess Champion for the Commodore 64 was published by Green Valley Publishing.  This is a pretty entry level Chess game with 7 levels of play.

Chess Master by John Krause (FHD Software, 1986) - Recently started watching some Chess matches on YouTube and what do you know, I stumbled on this Chess game.  This is nothing fancy, but there are 5 levels of play and you can also let the computer play against itself.

Colossus Chess 4 written by Martin P. Briant, published by CDS Software in 1985 - From what I've read in reviews, this is one of the strongest chess games you'll find for the Commodore 64.

Masterchess has been designed to be a no-frills chess playing program of advanced ability which is easy to use. Special emphasis has been placed on providing facilities useful to those wishing to improve their game as well as just pass a pleasant hour or three. To this end it is possible to review an entire game, step-by-step, or re-arrange the pieces to make a point, or even build-up a position starting with a blank board. Handy for solving chess problems, or practising your end-game!

* The manual for the game is inside the archive as a text file.

Modem Chess v2.0 by Bobby Smith and Mike Quinn is a classic chess game for the Commodore 64.  Contrary to its name, it doesn't require a modem, or even have the ability to use a modem.  This is a two player only chess game in which players hot seat to make their moves.