Private Browsing Window is a Firefox extension that permits you to start a private browsing session in a completely new incognito window alongside your existing session – like you do in Chrome. This extension greatly improves Firefox’s behavior as far as “private browsing” is concerned – before Firefox would automatically close all windows and tabs in a working session when you switch to the private browsing mode, all except one – the launched private browsing window, to get back a closed working session you had to leave the private browsing mode. With this extension private browsing and non-private walk side-by-side.
Private Browsing Window extension practically creates a new private_browsing enabled profile – without your bookmarks, browsing history and preferences. In my Ubuntu 9.10 the new private window opens with the ‘Ubuntu Start Page’ as my home page instead of Google. In the Tools menu, ‘Stop Private Browsing’ and ‘Clear Recent History’ items are not enabled – you no longer need them.
Private Browsing Window also places a small shortcut icon in the bottom right corner of your screen.
[Update 3 April 2013] Newly released Firefox 20.0 comes with Per-window Private Browsing, that “emulates” this out-dated extension.