Our 4 1/2 year old did the same thing! He started chewing when he turned 3. He chewed his nails down to the quick! I tried to keep him from doing this until about 4 months ago. I got on to him constantly. We applied "Thum" (You can get it at Walgreen's). Nothing seemed to work. When he turned 4, he started picking his nose and eating his little treasures...that is when I started focusing my energy on the newer (less acceptable) behavior! I noticed that 2 of the 3 physicians my Dad treats with also bite their nails! I thought, "If my son becomes a cardiologist, I will consider myself crazy to have obsessed about his nail-biting habit!" Just within the last two weeks, our son stopped biting his nails! I actually had to trim them two nights ago!
I hope this helps! Good luck!
J.