I did some messing around with the DOM Inspector add-on to find out the XUL pages that the IRC uses.
I have no perfect solution, but one of these two might do:
Solution 1: Set the homepage of Firefox to
chrome://chatzilla/content/chatzilla.xul. This will automatically open the Chatzilla IRC client in a Firefox tab. The downside, of course, is the fact that the ChatZilla IRC client will be inside a Firefox tab, which means that the top part of the window will be Firefox (and take up some vertical space). Of course, you could hide the navigation bar and do some other tweaks to hide the top part of the window.
Solution 2: Set the homepage to
irc://. This will automatically open the usual ChatZilla client but you will still have to close the Firefox window. But this does cut one step and therefore better than nothing.
EDIT: I have found the perfect solution! (Windows instructions)
Right-click on the shortcut of your Firefox icon and go to Properties.
In the shortcut tab, Target field, ADD this to the END of the target:
-chrome "chrome://chatzilla/content/chatzilla.xul" and press OK.
If you still want to use Firefox for regular web browsing, I would make this as a new shortcut. Or at the very least, change the name and icon of the shortcut to ChatZilla so you know what you are clicking on.
EDIT2: A quick search showed that you could simply use
-chat at the end of the target. I suppose you would have already seen this, which means that you only wanted to know how to add it to the jumplists. You could try the Jumplist Extender.