Invision Power Board (the 3rd party message board that FBG uses) has two different types of chat plug-ins. One is called parachat and the other - I forget the name. So it's definitely possible to add-on. You can have multiple chat rooms up to a certain number of individuals per room.
From a business standpoint, chat would be counterproductive because on a message board, you check back multiple times a day for responses to threads, new thread topics, etc. Every time you do that counts as an impression and the Players Network pays their associates based on impressions or click-throughs on ads.
Chat is more difficult to implement advertising into without a live mod plugging it in every so often. I'm not pretending to speak for FBG, just offering a possible explanation as to why chat would be bad from the business side of things.
All this is true, but chat can add to revenue through increased user base and improved user loyalty. Basically chat can help you get new people and keep existing people from going elsewhere. Usually with a user base this size the cost associated with chat is less than the benefit provided. It also allows for expanded opportunity for staff/user interaction, for example trivia contests, guess the next draft pick, charity auctions, live interviews, etc. Most of that can be done on the message board, but chat give greater flexibility.