Can I get desktop notifications for Chat?
Every agent has the option to enable Desktop Notifications (a Labs feature) for themselves, if they wish. You can find this setting under Chat > Settings > Personal > Sounds & Notifications, and it looks like this:
You can enable notifications for any combination of the above settings, according to your preference.
You should also ensure that the page in question has permission to send notifications. In Chrome, you can set this for the page by clicking on the icon to the left of the address bar:
For other support browsers, you should consult the appropriate documentation to confirm notifications are not being blocked.