My daughter appears to have an allergic reaction when she eats chicken. is this common?

No, but possible: One can be allergic to virtually any food, but some foods are commonly allergenic (especially dairy products, gluten, eggs, corn, soy, almonds & peanuts) & many rarely cause allergies, including chicken. However, most chicken is raised with hormones & antibiotics & fed genetically modified corn & soy, and it is possible the sensitivity is to those substances. See if she tolerates organic chicken.

Possibly: Poultry allergy is not common but i just evaluated a child with it yesterday so it happens. If your child also has an egg allergy that would increase her chances of developing the chicken sensitivity. If you are suspicious, read all food labels and avoid chicken in her diet and contact your local allergy specialist for an evaluation.