Google just released a New Hangouts App for Chrome Browsers and Chrome OS for Desktops. The App packs many UI changes (than the old extension) it also packs floating chats similar to Facebook's Chatheads feature, but for your desktop.
The premise is simple as the demo video below shows, a Hangouts bubble floats on the side of your desktop, opened from Google's Chrome app launcher, and subsequent conversations float above that. Users can click and hold to drag the bubble around and manage/participate in chats just like on the web.
Native app experience. Hangouts runs in the background and notifies you of new messages and incoming calls with animated notifications. Launch Hangouts from the Start menu, have it pinned on your taskbar and switch apps using Alt+Tab. Download it to your Desktop Chrome from Here!