Set up a grill for indirect cooking over medium-high (see note below). Clean and lightly oil hot grill. In a bowl, combine paprika, ground pepper, salt, cayenne, oregano, thyme, garlic, and oil; rub on chicken.Advertisement
Grill chicken, skin side down, directly over heat source until skin is browned, about 4 minutes. Flip chicken; move to cooler side of grill. Cover grill and cook chicken until cooked through, 35 to 40 minutes. Transfer to a platter and tent with foil. Let chicken rest 10 minutes.
Indirect Grilling: This setup creates ovenlike heat and is great for larger pieces of meat or foods that require gentle cooking. Arrange coals on one side of the grill, place food on the other, and cook with the lid on. Or preheat a gas grill over high, then lower heat on one side to medium-low or off.