Love this Chick-fil-A location. I have no problems with my allergies, they are so careful to prepare my food with care!
For Gluten free try a salad and just use lemon for a dressing. Or the grilled chicken nuggets. See ingredients:
Grilled chicken (whole breast filet, seasoning [water, apple cider vinegar, soybean oil, yeast extract, salt, modified corn starch, palm oil, dehydrated garlic, dehydrated onion, corn maltodextrin, sea salt, flavor, sugar, chicken stock, cane molasses, chicken fat, spice, natural flavor {including smoke}, dextrose, lemon peel, citric acid, red bell pepper, orange juice concentrate, grape juice concentrate, natural flavor, paprika, vinegar, xanthan gum, ascorbic acid, and spices]).