Edit:
I found a very hackish but surefire way to hide the panel indicator.
Simply replace the stock indicator with this one-pixel transparent PNG file (right click → Save link as to download the file).
Instructions on replacing the indicator may be found here.
Original answer:
There are various discussions about this on Google's product forums. The only solution I've found that partially works is to disable Google Now in Chrome's flags:
- Navigate to
chrome://flags/#enable-google-now
- Set the flag to Disabled
- Restart Google Chrome
However, even with this flag disabled the notification icon can reappear under some circumstances:
The Notification Bell seems to reappear consistently when i fullscreen
a Youtube Video, even after deactivating "Google Now" and anything
that even mentions "Notifications" in the flags settings.
--- Source
Google's official statement on the matter isn't very satisfactory, either:
Hi All,
As mentioned on the flags page, those are experimental tools that can
get removed at any time. We are working on improving the notification
system and your options around controlling when to see them, which
will be included in upcoming releases. For Windows users, please try
clicking on system tray, customize link, which will open your control
panel. You can then change the settings for your notification area
icons for Chrome from there.
- Sarah
--- Source
I guess we will have to wait for now.