Does anyone actually own the Rights to "Chess"? I see tons of Chess apps/programs/sites charging for chess games and I am unsure if such things are legal.

The game is hundreds of years old. The concept and the rules are fair game.

Beware of implementation details. Making a specific clone of a specific version, such as the popular BattleChess, is a different risk.

The oldest written references to the game of Chess date from before 600 AD, in Northern India or Afghanistan. Nobody owns it.

The oldest written references to the game of Chess date from before 600 AD, in Northern India or Afghanistan. Nobody owns it.

Impressive.

Be aware though that someone might own design of chess pieces, specific appearances of the Queen and knight piece etc, so be careful where you get art and models. Similarly the board will be OK if kept simple but if you copy a unique board from a different implementation of chess or a chess like game you may be lining yourself up for trouble.