An allergy is your body's way of dealing with a unknown protein. It uses an inflammatory response to drive out these foreign invaders that it does not know what to do with. Robyn O'Brien talks at TED about the rise of food allergies and it's link to deadly diseases. It is the genetic engineering and added hormones in commercially process foods that can be the explanation for this.
It may not be that your dog is allergic to chicken, but it is allergic to the hormones or steroids in the chicken.