I have narrowed it down to google chrome
Can't move my pieces in online chess.

Yes, it seems certain Google Chrome extensions cause this effect.
I was having this problem until I disabled the WiseConvert extension.
When you have identified the dodgy extension, click on Tools {spanner symbol} -> Settings -> Extensions and Disable it.
Someone else identified utorrentbar as the culprit.
I can open up my online games, but I can't move the pieces to the spot I want to move them