This was happening to me too and it was driving me crazy!
In my situation (trusty), this had nothing to do with user profiles. My issue was that the desktop environment was shutting down prior to the background chrome process; this caused chrome to ‘ungracefully’ exit and bug me about it with each restart.
Some of the solutions you find on line get around this by never letting chrome run as a background process, which was an unacceptable trade off for me.
I fixed it on my system by adding a stanza to the Upstart script for the desktop manager (Lightdm). You need to edit /etc/init/lightdm.conf as root:
sudo nano /etc/init/lightdm.conf
Add the following at the end of the file:
pre-stop script pkill --oldest chrome sleep 2 end script
Hope this works for you!
Credit: MadMike, posted at https://askubuntu.com/questions/248496/google-chrome-does-not-quit-nicely