Use the adverb volubly to describe the way a chatterbox talks. You could talk about your uncle Bill's habit of speaking so volubly that no one else can get a word in.
If you know someone who talks incessantly, you can say that she chatters volubly. A whole roomful of preschoolers sometimes talks volubly, and a talk show host might be hired because of her ability to speak volubly on a wide variety of subjects. The Latin root word is volubilis, "that turns around, rolling, flowing, or fluent," which in turn comes from volvere, "to turn around or roll."