Always On Top (compact chat window) option - so I can work on another full-screen app while still seeing chat with co-worker.
If chat window can be made small and float to front (AKA "always on top") then I can work on a full-screen tool (IDE, graphics design tool, large doc editor) while still being able to see what a colleague is typing. I should still be able to minimize the window to the taskbar, and I should still see some visible notification when new chat text arrives while the window doesn't have the input focus. In my desktop context I often have the chats open on a second screen, but I don't tend to bring a second screen when I am travelling with my laptop.
This is another request for a feature that OLD versions of Skype were able to do just fine! Since MS started to mess with it usability went all the way downhill!
Sean Ellis commented
For this to work well, this must be maximally compact, and should ideally have separate font settings from a regular chat window.