Games are patentable subject matter in the U.S. and have been covered by both apparatus claims and method claims. There are many many patents on "proprietary" card games involving betting that are variations on poker, etc. There are patents on method of playing certain board games.
The fact that chess, as is normally played, is old does not mean one can't come up with a new game that is similar but different from chess.
However, after the Supreme Court Bilski decision the art unit at the USPTO responsible for game patents seems to be taking the position that it is all abstract and they will no longer allow anything unless you appeal and win the appeal. If it is "computer implemented", then arguably a machine is involved and that might be seen as not abstract.
Also you can have a board game considered if you have some unique, functional physical structure to the game pieces. That would not be your case if you are using standard chess pieces. I did see a patent on a game with pieces that could come apart. If you lose an arm in game play, the piece looses an arm.
Here is a patent on a non-standard way to play chess. The claims only cover a computer implemented version.