H.L.
My daughter is 9 and started biting her nails (including toe nails) at age 2. I don't know what started it and the doctors (unsettlingly) aren't worried. I told her about all the nasty stuff that lives under your fingernails...while that stopped her for about a week, she is back at it. Thank God she stopped biting her toe nails!!! I paint those and she knows if she chews her nails she can't get them painted anymore.
There is a Sally Hansen nail biter "polish" that tastes NASTY, my mom used that on me...it worked because even hand washing didn't make the taste go away. I stopped using it when I got pregnant because the smell bothered me, and once she was born, I didn't want to accidentally get any near her mouth...
Tobasco also works, but if your child rubs his eyes, that's not a good idea. The Sally Hansen didn't bother my eyes on any occasion I had to rub them.