The Gmail Favicon Alerts 3 user script works on Chrome, as well as Firefox and Opera (although I haven't tested Opera). It will show up to 999 new messages, and works on Gmail and Google Apps, even if both are opened in tabs.
A little bit late, but since I found this as the first result when searching for this very issue, I should add that it's possible.
Set up the priority inboxes and your labels, if they aren't already.
Apply a filter to archive "work" messages coming in so they skip the main inbox.
Go to Settings > Inbox > Options next to the inbox section you want to customize.
Click "More Options..."
Right-click or CTRL+Shift+C on the label (e.g., "work") and select "Inspect element." (Firefox users just go to Tools > Web Developer > Inspect Element and click on the label).
Look for the attribute cfg="^all,Work" and change the value to cfg="^u,^all,Work"
Finally, select the work label on the page as normal.
Best Answer
Search for;
OR
in your Gmail search box.
Other Gmail search operators can be found here;
http://mail.google.com/support/bin/answer.py?answer=7190
Hope this helps