C.C.
Like the Previous poster, I'm just here to tell you that you are not alone. My daughter will be 6 soon and has been doing this for months! It started out just as finger nails to the extent that her fingertips were red because she'd bitten so far down`. It seems that shes done with the fingernails, but now she has her fingers (not even chewing), her coat, her toys, her pencils, etc. in her mouth. She actually put her fingers in her mouth as we were preparing her second taco! It's less than one minute between the food she finished chewing and the food she will begin chewing! It drives me insane.
Also, at a birthday party this weekend, I told her to put her fingers down and two other moms also confirmed the same issue with their daughters. Looks like we may just have to wait it out. Good luck to us all. =0)