Light a gas grill. Wrap the hickory wood chips in heavy-duty foil and pierce the packet all over with a skewer. Add the foil packet to the grill. Cover and let the wood chips begin to smoke, about 5 to 6 minutes.
Brush the chicken with oil and season generously with salt and pepper. Cover and Grill the chicken, over moderately high heat, turn and shift the pieces occasionally, until lightly charred and cooked through, 35 to 40 minutes. Transfer to a platter.
Let’s make the sauce: take a medium bowl, whisk the mayonnaise with the vinegar, horseradish, lemon juice as well as garlic powder and cayenne. and season with black pepper and salt to taste. Transfer the barbecue sauce to a pitcher and serve with the charred chicken.