The Digital Inspiration blog suggests that Facebook's new browser-based chat system, which we stood up against Gmail's web chat yesterday, works well running inside a Firefox sidebar. To anchor it there, simply add this Facebook Chat popout URL from Bookmarks->Organize Bookmarks, and make sure "Load this bookmark in the sidebar" is checked. The intended two-column layout can make the sidebar a little intrusive into your actual browsing, but you can resize to a narrow strip and still get chat functionality, simply by clicking inside the sidebar to re-order things.
Put Facebook Chat in Firefox Sidebar & Talk from Any Web Page [Digital Inspiration]