Here's an article that tells how:
https://support.chess.com/customer/portal/articles/1444877
How to Block member
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Nov 15, 2015
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#3
http://www.chess.com/home/privacy here you can just type the people you want to block.
Disabling chat blocks everyone from chatting. How to block only specific users, from the mobile (iOS) app? I know how to block from browser; there should readily be a block button in the user profile drop down menu in the mobile app.
How to block a member who uses offensive language while playing