Another possibility is to is to use the Show/Hide UI toggle to remove most of the rest of the UI from the main view so you can maximize an unblock main view. This toggle only toggles the visbility of the UI the is built-in with the official viewer. It does not toggle visibility of the Icesphere's UI. This allows for futher alternatives to the default UI for those that wish to have such freedom.
When you start Icesphere, after you logged in-world, you'll notice in the system tray (or in the status icon bar) a sphere that is for Icesphere. In the above screenshot, it looks like a blue sphere. Click on the icon and you'll see a menu popup with an option for "Show View" as well the toggle for the "Snowglobe UI" option. Bring the mouse over "Show View" and you'll see another popup display a list of windows you can show. At version 0.10.1, these windows normally default to hidden when you start Icesphere. If you click on "Communicate" then you'll see the chat window (shown above). Notice I have already hidden the UI from the main view with the "Snowglobe UI" toggle. (*Ack!* My status icon bar is cluttered with shortcuts, but normally all those icons are hidden out of the way.)
If your just doing chat, then I find the layout above works really well. I can use either alt-tab or the mouse to switch between the main view and different chat sessions.
In the upper-right corner of the Communicate window is a 2 buttons side by side. These work as expected to detach the chat sessions further or close individual sessions.
Also note that you can use your Input Method (or GTK's input method) on these chatbars. It should default to your desktop's settings, or you can right-click the chatbar input area to select other Input Methods. Currently, the main viewer doesn't support all input method and bidi formats, so this should provide an alternative to allow such flexibility.
At version 0.10.1, the popup menu might not be the most intuitive, yet it provides the default access to Icesphere's functionality. There are plans to enable toolbars and action bars that'll allow you customize the UI more. So far, there has been more backend work to ensure Icesphere and the main viewer work smoothly together.