Preheat your grill to medium-high heat.
Rub the chicken breasts with olive oil and season evenly with Cajun seasoning, paprika, salt, pepper, garlic powder, and onion powder.
Grill the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F.
In a bowl, whisk together mayonnaise, apple cider vinegar, Dijon mustard, horseradish, lemon juice, Worcestershire sauce, black pepper, and cayenne pepper.
Drizzle the Alabama white sauce over the grilled chicken or serve on the side for dipping.
Enjoy with your favorite sides like grilled vegetables or cornbread!