OBS.Live does have some other neat features, too, including an activity feed and even music controls, but even if you only need Facebook Gaming chat, it's worth getting.
Simply download the plugin and authenticate your Facebook account, and you're set. But even if you're not, it's free to use and will let you have a Facebook Gaming (it supports Twitch and YouTube, too) chat window inside OBS Studio. If you're using StreamElements for your alerts and overlays already, it's a no-brainer.
The answer is StreamElements' OBS.Live plugin. But, despite having no popout chat feature on the website, there is still a straightforward way to get Facebook Gaming chat inside OBS Studio.
