Limit Those Who Can Post in a Chatterbox

Is it possible to limit who can post in a Chatterbox? For example, the General Chatterbox contains all members, so only a select few are able to post in it, but all can receive the notification.

I could see this used as we return from a campout to provide and ETA for pickup, Summer Camp updates, etc.

No, it is not possible to limit who can post. Chatterboxes are intended to be a Chat platform where people can chat back and forth.