I'm a former 4th grade teacher. I use to deal with many chatty girls who just wouldn't focus in on the school work. Instead she is focusing all the work into socializing.
My question is how is she with her social friendships? Does she have friends in the class or is this her way to try to get friends? When the issue is in the socialization, it's important to understand what is happening in that arena. Could be something going on there.
Sounds like she is capable of doing the school work (teacher says she is smart etc)- and if she could only refocus her socializing, then her work wouldn't suffer.
If you don't know socially what is going on, I'd try to find out. Sounds like there is some underlying reason as to why she feels the need to get the socializing attention during school lesson time. Find out what that is and refocus her behavior there.
Another idea to at least try....If she is a good student with her work -- make her a peer tutor to other students. This is what I did in my class for my chatty cathy, make them the peer tutor and have the responsibility and discipline they have to show in the class time. In other words, refocus the social behavior so that it will be channeled into the schoolwork -- and maybe you will see her improve that way. This idea of course, you would have to work out with the teacher, but it may be at least helpful and something to try.