Recently I reinstalled the Hangouts-application for Google Chrome. Afterwards i noticed a small Chrome alert icon, symbolized with a bell, on my system tray. Apparently no remove or disable option where available. However, I did manage to find a solution.
1. Type "chrome://flags/" in Google Chrome search field.
2. Find "Enable Rich Notifications Windows, Chrome OS". Change setting to "Disable"
3. Restart Google Chrome
The icon is now removed from your system tray.