There are a number of desktop application are present on the internet to download for free and use for chatting purpose. Digsby is the best example of these type of softwares. Its a multiprotocol instant messaging application, which enables you to use Yahoo, IM, Facebook, MySpace and some more online chat services in a single platform. There are some more Apllications are there to use facebook chat on desktop like ScrapBoy, MirandaIM, ChitChat, Yoono etc. These all are free softwares, which you can download from their own website and use for facebook chat.