I have a friend that won't stop talking

We both study the same program and are both females (25).

My friend is nice, well-meaning, and thoughtful (in most ways that matter). However she talks SO much. Like almost to the point where it's concerning. If she could she could hold a single line of speech for 6 hours probably. She cuts other people off mid sentence, does not let anyone in. Talks during classes and other times where it's not really welcomed by the listener.

A lot of people in the study program are pretty much sick of her. They find her rude and exhausting. I just found out, because they didn't feel like they could badmouth her to me. They can't really but I recently had the leading role on a project with her and other people where they voiced their opinions, and thus also personal opinions.

I have been so patient, but I'm getting SO sick of it. It's so draining to the point where I cry after a few hours of seeing her. But how do you voice this without shattering her poor self? I feel that If I want to call myself a morally right and good friend, that I should tell her the deal. But Is it possible to change someone like that? Has anyone had actual success?