I bet she has a high IQ! I have similar issues with my son, since Kindergarten, he's now in 5th grade and it's still a struggle. Some teachers he has been great with others not so great. My first suggestion is ask for a referral to the school counselor. The counselor can help teach your daughter some tips to controling herself. You have to understand that it's very difficult for her to control herself and sometimes impossible. That doesn't mean they can't learn to control themselves it's just very very hard!
A few other things that have worked for us is having my son at a desk that is apart from groups. Although the teachers don't like to do this because they are supposed to have the kids in little clusters, but this has really helped my son because it takes the temptation of talking away and he expressed to me that it is helpful to him. Then he does join the groups for group projects but is on his own for individual learning. Another trick is he has an extra notebook to jot down his questions and thoughts during the day, the teacher reads and responds to his thoughts. That way he gets validation for ideas and observations that he can't share with the class. This may be a little advanced for your daughter but maybe she can have a notebook that she can write things down in once her school work is finished. (As I'm sure she finishes well before everyone else and is then tempted to talk.) Ask the teacher to give her extra work, exercises, word searches etc. If she is finishing too soon this will help her stay busy until the rest of the class has caught up.
Make a chart for home that she gets stickers for everyday that she didn't get a mark for talking. I know when my son was in kinder they had clips that would be moved if they were talked to about something. If he didn't move his clip and stayed on green he would get a sticker. If he had 4 days in a week he would then get a small prize. Small weekly goals work better at age 6 than monthly goals but as she gets older you can change them. I made a chart using Excel and bought some cheap stickers, but they do sell dry erase board type chart for this type of thing.
All of these tricks have worked for my son, but it's a constant juggling game to get the right combination when. As long as your daughters teachers are willing to work with you and her and see that you are willing to work with them you should be able to get through this just fine!
After reading some of the response I wanted to add that a great book that helped us was Parenting the Strong Willed Child:
http://www.amazon.com/Parenting-Strong-Willed-Child-Rex-F...
This was recommend to us by a child psychiatrist that evaluated my son at about age 5 or 6. Although this book is geared towards younger children, there are a lot of good tips that really helped us. The main thing is to be consistent in your discipline, 1 warning then consequences. And make sure to not threaten something that you are not willing to follow through on. Please don't listen to Christy's advice, which is absolutely ridiculous!