Chick with one leg. Itching problems?

[UnfortunateChic]

So I was at ATwoods and saw a small chick with it's right leg sticking straight out to the side. it was just a hatchling. Over the past week or two it's gotten really good at standing and supporting itself against the cage and it's leg is even showing signs of possibly being able to touch the ground when the chick stands, i mean, it's fully functional it just sticks out to the side.. Although i'm glad it's doing well it cannot scratch it's face on that side and it's driving the chick insane. I've rubbed the side of it's face, looked for any agitators and have came up short. I have no idea what to do for it and i would HATE to cull it for reacting so badly just because of a simple itch! I'll try to scratch and when it cant it'll fall over from lack of support and squirm around on the ground trying to get it's foot close to it's face. after that it attempts to relieve the itch by scratching the opposite side of it's face and i'm afraid it's going to hurt itself because it's so violent. Any thoughts suggestions ideas? What do your one-legged chickens do?