Well this is awesome: Gmail just added desktop notifications baked directly into Chrome. Here's how it works.
Basically it turns Chrome into a desktop notifier for Gmail, so you don't have to run any separate notifier if you're big on getting the heads up when new email (or chats) arrive.
To turn them on, click on the Settings link in the top right corner of Gmail and scroll down to the "Desktop Notifications" section. If you just want to get notified about chat messages, or if you use Priority Inbox and only want to get notifications for important messages, you can customise your settings from there too.
Clearly this is also a good thing for Chrome OS, which isn't capable of running regular background apps, but can background web apps—and display their notifications. Spicy.
The new notifications ship with the ability to toggle chat notifications and choose between notifications for any new mail, or just for Important mail (that is, email that hits your Priority Inbox).
Desktop notifications for emails and chat messages [Official Gmail Blog]