Sorry about your chicken's neck. My Golden laced Wyandotte survived a raccoon attack in the coop about 2 months ago. The back of her neck was badly bitten - about a dollar coin size, and deep. There was not much blood, but you could see way down through the layers of fat to the neck itself. She was very slow moving for about three days, and didn't eat or drink (that I could see) for 2 days, but I coaxed her to take some feed from my hand (she was accustomed to that from a chick), and she steadily improved over the course of about ten days, to the point where she is fully recovered now.
I didn't give her any oral medications, just poured some hydrogen peroxide over the wound on the first couple of days, and then on day 3 and 4 as it looked like it actually might start healing, I smeared some over-the-counter antibiotic ointment over it. I don't know if any of that helped, but we are so glad she recovered.
Of course it took a while for her feathers on her neck around the area to settle down, and most of the feather have grown back now, but there is still a small scar where I don't think she'll have feathers again.