Why is Chess.app "required by OS X"?
I don't use it, and I can't delete it. Is it really required by the operating system?
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Later Mac OS versions have SIP enabled, which prevents you from simply
sudoing your troubles away. What you have to do now is:
Cmd-R, which should eventually boot you into recovery mode.
csrutil disableto disable SIP.
cd /Applications/ && sudo rm -rf Chess.app/
I have deleted Chess.app from every version of Mac OS X and OS X that I've used starting with Mac OS X 10.4.x and have never had an issue from doing so.
You can use AppCleaner to do it, although you first need to uncheck  Protect default apps in its General Preferences.