Let's not forget that this is first grade and that kids who are naturally more gregarious have a difficult time restraining themselves from all the social contact available. You are fortunate to have a teacher who sees this situation being caused by your son's personality needs and not by some clinical problem he should be medicated for (your pediatrician's advice concerns me, given hyperactivity should be one of the last things investigated when a child presents as your son).
I would work with this teacher in attempting to find acceptable daily social outlets for your son. Perhaps he could be the one who recites the instructions to certain daily assignments to the class. Maybe he could assist her at recess by thinking of interesting ways the kids could line up every day- alphabetical order, hair color, ascending numbers of their street addresses, etc.. Perhaps he could be part of a small group of kids who performs a little skit every day that has some relationship to a lesson. He may be able to take some pride in these assignments while channeling some of his need to be social, outgoing and connected more often to other kids. That's the route I'd go. As an afterthought, make sure his talking is not an escape from doing work that he is finding too difficult. For instance, many kids (especially boys) in first grade have problems with the fine motor control needed to hold and/or use a pencil. They can't work fast enough to keep up with written work, stop trying, talk in class or claim they are bored.
Good luck brainstorming with the teacher and thanks for writing.
