Chick-fil-A offers gluten free grilled chicken nuggets and many locations have dedicated fryers for fries. Check with your location if cross-contamination is a concern for you.
BEWARE!!! ABSOLUTELY UNSAFE AND CROSS CONTAMINATED!! Glutened AND food poisoned in one trip just because I tried the fries. The fries ARE NOT GLUTEN FREE!!! The oil is filtered through the same system as the oil used for chicken. I threw up very quickly afterwards and was violently ill for a full day and it took me a week to recover from being glutened. DO NOT GO HERE UNLESS YOU LIKE BEING SICK!!! Even the grilled chicken is cross contaminated!
Ordered gluten free bun told them I needed glove change they gave me a sandwich with a gluten bun. Went back and told them I needed a new sandwich with a gluten-free bun. Gave me a gluten free bun but a breaded chicken sandwich instead of grilled. Went back and explained to them how every other chick fi la does it and they finally got it right
This was a very good experience. At the counter I specifically said I had a gluten allergy and they immediately got the manager and ensured that gloves were changed, minimized cross-contamination, and made my order separately. I have been there several times and have not had a reaction at all.