Tennessee law - HOA Board meeting

I am part of the BOD of a new HOA. I was recently asked that our BOD meetings need to be public or allow observers. Now this request is coming from a non-stop causing trouble member and even though it's 1 out of 35 members making such request I want to provide a valid answer. Our bylaws and CC&R do not mention anything of that sort and the TN non profit act doesn't either.
Our board announces the meetings and provide minutes to the association shortly after so we are pretty transparent in how we do business so far.
Is there a sunshine law in TN that will make us as board having to allow observers in our meetings??

Most likely the bill Richard pointed out will become law. In most States the BOD meetings are open and can be attended by any member who wants to attend. Notices of the meetings and agendas must be published to the members. Most likely your state will also move in this direction. However, the attendees do not participate in any vote and in most states the HOA just has to allow a short time frame (can be limited by such as 3-5 minutes to speak on a concern). After they speak the BOD simply states, your comments have been noted and the BOD will review. What I have found is usually NONE attend. LOL ... Even in my local City Council Meetings sometimes I am the only individual in attendance. My suggestion would be to go ahead and get used to what the proposed legislation allows because if your state has not already passed it will shortly. It will be good practice for the future...

What Janet said. It's good that you're being transparent with everything else - having open board meetings can be just as beneficial because people will be able to see and hear the thought process behind a decision.

The main issue is keeping control of the meeting. You can have a resident forum at the start where everyone will get 2 minutes or so to speak their piece about an association issue. After that, remind everyone this is a business meeting, therefore no comments are questions will be taken from the floor so the Board can address everything on the agenda. Cell phones off or on vibrate (and take the call outside so you don't disturb anyone), no cursing, yelling, threats and other obnoxious behavior. Violators will be asked to stop and if they refuse, be asked to leave. Publish those rules and have the president announce them at the beginning of the meeting.

This should take care of the bulk of the problems - if this homeowner doesn't pay attention and frequently disrupts the meeting, you could ban him/her from attending (talk to your association attorney first and be sure all the bad behavior has been documented in case the homeowner wants to push things even further).