You can sit her down and tell her there is a time to talk and time to listen. Don't be harsh, because she doesn't realize that it's problem, but just tell her that in school she needs to limit her talking, while doing independent work she needs to focus on her work and not distract others...Even when she's done, others may not be so she shouldn't pull THEM away from their work, even if she's doing really well. Tell her to keep others in mind and that every thought that comes to her head doesn't necessarily have to be spoken.
You can tell her that after she's done with work she can write in a journal about what she's thinking -just as long as it doesn't become a problem in class and she's not using it while the teacher is teaching...
Tell her that talking is not a bad thing, when it's at the RIGHT time...let her know she's not in trouble or she's doing something bad because she can't help it...