I wouldn't say all the messages are dumb; I have had some very rewarding conversations in chat. But there are times where I want to just focus on the game too.
See below in your settings: Live Chess: Game chat needs to be set to Friends Only or Nobody for you to fix this and not receive any chat messages.
For live chess, I turned off both sets of chat setting that I can see, thinking that would mean people couldn't send me chat messages during games. However, I still get both chat requests, and other chat messages without the request icon. Sometimes the emoticons flash up also. This is via a browser. I've logged out/in, refreshed, cleared cookies, restarted etc., to no effect. Can disable chat in the game itself via the x button, but then you need to do it every time. Any other solutions? The messages are all dumb and I could do without them. Thanks.