1. Go ahead and head over to your extensions page - chrome://extensions/ (paste this into your browser address bar and hit enter) - and completely remove Hangouts.
2. Close Chrome
3. Restart Chrome
4. Head over to http://hangouts.google.com and click on the left hand side for the menu. Select the Chrome icon and re-install Hangouts fresh to see if this solves the issue, (You can download the App from the left-hand menu if you don't wish to use the web client!)
It's very important to do ALL steps, even if they seem redundant ;)
Hope this helps!