Is it possible to add a button to a tabbed pane like in firefox.

The plus-
I think you should be able to manage it by building your own JTabbedPaneUI and setting it on the JTabbedPane using setUI.
Your ComponentUI has methods to get a hold of the accessible children. If you specify a JButton and a JLabel then you may be in business.
I haven't attempted this myself though. This is "at your own risk" :)