In a stainless steel pot, melt the butter slowly over low heat.

Add cider vinegar, ketchup, prepared horseradish, lemon juice, salt, Worcestershire sauce, and hot pepper sauce (if using).

Stir to combine.

Simmer the sauce, uncovered, for 20 to 25 minutes, allowing the flavors to blend and the sauce to thicken slightly.

Preheat your grill to medium-high heat.

Season the chicken pieces with salt and pepper, if desired.

Place the chicken pieces on the preheated grill and cook until they are cooked through, turning occasionally and basting with the barbecue sauce during cooking.

Continue to baste the chicken with the barbecue sauce until it is fully cooked and has a nice caramelized exterior.

Serve the grilled chicken hot, with any remaining barbecue sauce on the side for dipping or drizzling.