I'm going to disagree with some of what has been posted here and say your chatty coworker may not "need to be heard". She may be driven to talk, with or without an audience.

http://en.wikipedia.org/wiki/Logorrhea_(psychology) explains what is probably going on

For your own sanity, stop listening and stop paying attention to how much time she spends wasting time. Wear headphones or earplugs if and when you can, and in training sessions, you have every right to ask her to hold her comments because you are trying to listen to the instructor. I'd say it nicely the first time, during the training, and more tersely a second time, during the training. Trainers have an obligation to control their audience; and if your job depends on such training, you have the right to be trained properly.