Would it be possible the save the Tabs Outliner's window's position in the list?

As the title suggests I like the idea of having the Tabs Outliner window at the very top of my window list and having it remain there even when I reopen Chrome (which happens quite a lot). You can only have one instance of the TO popup window anyway and you can't open another tab in that window (a new window is created as a parent instead), why not just save it? I'm pretty confident that this is possible.