In a mixing bowl, combine mayonnaise, vinegar, mustard, sugar, garlic, and horseradish. Whisk until smooth. Set aside half for marinating the chicken.

Place chicken breasts in a zip lock bag and pour in the reserved sauce. Seal and massage to coat. Refrigerate for at least 4 hours or overnight.

Preheat grill to high heat (450-500°F) at least 30 minutes before cooking.

Remove chicken from bag, rinse under cool water, and pat dry. Brush with olive oil and season with salt and pepper.

Place chicken skin-side down on grill, cooking for about 2-3 minutes until grill marks appear. Flip and grill for another 2 minutes.

Move chicken to cooler part of grill skin-side up, reduce heat to medium, and cover. Cook for 15-20 minutes.

Baste chicken with reserved sauce every 5 minutes and monitor internal temp for 160-162°F.

Once cooked, let the chicken rest for 5 minutes before serving with extra sauce on the side.