Facebook has a messenger app for browser which works nicely. But it will be really great to have a standalone Facebook messenger for Mac OS X.
If you want to have a standalone Facebook Messenger, then download "Messenger for Mac"and install it in Mac. It is a free open source web-app which works flawlessly and serves it's purpose. It is not an official Facebook product. It is a free and open-source project which is created by the fans of Facebook Messenger.