http://support.chess.com/Tickets/Submit
Is there any way to report people for abusive language in the live chess app?

just disable chat. The admins will tell you the same thing. Most problems can be solved by just going mute:)

You can block up to 200 members under HOME - Account - Privacy Settings
http://support.chess.com/Knowledgebase/Article/View/38/0/how-can-i-block-another-user
I was just playing a game and he used the N word and a few other bad words, but he spaces them out like th is, so the site can't pick it up.