To turn off the new notifications, you have a couple different options. First off, you can just disable the Google Now notifications:
- Click the bell icon in the lower-right corner of your screen on Windows, or in the menu bar on your Mac
- Click the gear icon
- Uncheck the “Google Now” box
That disables the Google Now notifications but leaves other Chrome notifications. However, if you want to purge your computer of all Google’s obnoxious (to some) notifications (and that bell icon you didn’t ask for or permit to exist), you need to do one more thing:
- In Chrome, type
chrome://flags
into the URL bar - Search for “Enable Rich Notifications” and “Enable Experimental UI for Notifications” and set both to “Disabled”
- Relaunch Chrome