I think I have a chatterbox at home too!
My son would do that just to get attention. He doesn't like to be left out of the conversations. We keep telling him it isn't okay to butt in when adults are talking even though he said "excuse me".)
He has to wait until we finish. We would make conversation short. If he still interrupts the conversation, we simply tell him we will go talk elsewhere and he can't come with us.