Chicken-snake and rat-snake are essentially the same thing: a eastern corn snake. Some people will tell you that a corn snake and a eastern king snake are the same, some will swear they are related but different. Either way, that is what you have. Not poisonous, they prefer to eat rats and other snakes, but concider eggs and baby chicks a fine delicacy. A good Roo or two can actually fend of a small or medium sized one, that one is NOT small or medium sized however, lol. My guess is that he tried squeezing through the wire looking for rodents and got pinched in. Couldn't go forward and his scales hung, preventing him from backing out. Your dog could still be a snake bite victim as many of the non poisonous snakes have a saliva that causes a histamine reaction, much like a cat's scratch will, resulting in local swelling, itching, and mild fever in an extreme case, but lasting no more than a few hours to a couple of days.