This is a long overdue feature that finally made its way into SeaMonkey
SeaMonkey 2.18 Beta 1, a web browser, advanced e-mail, newsgroup client, IRC chat client, and HTML editing suite, has been released.SeaMonkey 2.18 Beta 1 is a new major release in the series and comes with a couple of important new features, not to mention all the bugfixes made available.
Highlights of SeaMonkey 2.18 Beta 1:
• Private Browsing support has finally been implemented, but keep in mind that this is an experimental feature and it might not work properly;
• Private windows will never prompt the user, even if normal windows are opened in the background;
• A File/New/Private Window menu item has been added;
• The Google search bar favicon has been updated.
A complete list of changes can be found in the official announcement.
Download SeaMonkey 2.18 Beta 1 right now from Softpedia. Remember that this is a beta version and it should NOT be installed on production machines. It is intended for testing purposes only.