Stir olive oil with paprika, salt, pepper, garlic powder and cumin. Set aside.
Rub spice mixture on all sides of chicken. Also push spices under the skin, being careful to leave skin attached to meat.
Grease BBQ grates well. Preheat one side of grill to medium-high heat, leaving heat off on other side for indirect cooking.
Grill chicken, breast side down for 8 to 10 minutes until skin is cooked well enough to release from grill and grill marks are browned. Flip and cook another 10 to 12 minutes. Move chicken to indirect heat side of BBQ. With lid down, cook for another 20 to 25 minutes, turning occasionally, until an instant read thermometer inserted into thickest part of the inner thigh registers 180°F (82°C)
Remove chicken from grill. Let rest 10 minutes before carving.
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