L.R.
I agree with the person who posted about possibly seeing if she should work with an occupational therapist (OT). Some children just need to chew, and some even concentrate better if they are allowed to chew (my friend's son has a written school plan that permits him to chew on special "chewie" items from the OT while he is in class; it helps him focus on his work!). I would ask your pediatrician today for a referral to get her evaluated. This does not mean there is anything "wrong" with her, if it does turn out she should see an OT; it only means she processes things differently from many kids and needs to learn to channel her chewing instinct appropriately. Getting her evaluated also could rule out whether there are other issues, so I'd do it. Also ask them to check her for sensory processing; some kid are very turned off by certain textures while others just feel they "need" certain textures or actions like chewing.
Also, starting work on this now is a good idea because if you leave it too long, there is more for her to "unlearn" once she hits school age. You don't want her to be in school and find you're getting calls from the teachers that she is constantly chewing on pencils, etc. The chewing on hands also presents potential issues for raw and chapped skin as well as transferring germs into her mouth.