The oil that Chick-fil-A fries their chicken in, is 100% refined peanut oil.
Chick-fil-A uses 100% refined peanut oil for frying their chicken in as the 100% refined peanut oil provides the chicken with a neutral flavor and also a high smoke point.
However for Chick-fil-A Waffle Fries, the Chick-fil-A Waffle Fries are fried in canola oil in separate fryers.
Although cross contamination of the oils between peanut oil and canola oil is still possible.
The refining process though for the 100% refined peanut oil that Chick-fil-A uses to fry their chicken in, removes the peanut proteins, so the peanut oil is not considered a major allergen for people with peanut allergies.
However severe allergies still warrant caution.
So while the refined peanut oil lacks the allergy causing proteins for peanut allergies, extreme caution is still advised if you have peanut allergies, especially severe peanut allergies or other possible allergies, due to the potential for cross contamination in kitchens.
Most people with peanut allergies can eat at Chick-fil-A, as they use highly refined peanut oil, which has the allergy-causing proteins removed during processing, making it safe for many.
However, due to shared kitchens and other potential allergens (milk, egg, soy, etc.), it's crucial to consult your doctor and be cautious about cross-contamination, as some individuals with severe allergies might still react.