My daughter chews on her sleeves, how can I help her stop doing this?

I have been very patient with my daughter over this matter. She is 5 years old. I remind her gently every time I catch her to stop chewing on her sleeves. She chews so much that her sleeve will be soaked from wrist to elbow, or the entire front of her shirt will be soaked. I have tried rolling her sleeves up, then she chews the collar. I have gum on hand for her to chew instead of her clothing. I have even sunk as low as bribery (if she didn't chew on her clothes for 7 days in a row then she would get what she'd been asking for). We have had to toss a couple of shirts because she chewed holes into them. She has even chewed the corners of blankets. Any thoughts or other ideas? I've asked her why she does it, and she doesn't know. I really think it is not a conscious thing. She will do it while watching a show, or playing a game, or reading a book. I just don't want to throw away any more clothes.