Allergies and supplements containing allergic ingredients

Maybe, maybe not. Depends on, how sensitive he is, how much chicken is in the product, and how the chicken ingredient is processed. If it's a very small amount of chicken (low down on the ingredients list) and you dog's allergy symptoms aren't very severe, it might be worth trying, but if you're risking something like a nasty, raging ear infection or weeks of itching if it does trigger their allergies, it's probably not worth it. This will also depend on why you want to supplement and what you're trying to achieve, since in some cases supplements can make a huge positive difference and in others there's just not enough evidence to make the risk worth it.