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. 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 min. until skin is cooked well enough to release from grill and grill marks are browned. Flip and cook another 10 to 12 min. Move chicken to indirect heat side of BBQ. With lid down, cook for another 20 to 25 min., turning occasionally. Remove chicken from grill when an instant read thermometer inserted into thickest part of the inner thigh registers 180°F (82°C). Let chicken rest while grilling corn.
Break ears of corn in half and season with paprika, salt and pepper. Lay a sprig of thyme across each cob and wrap with a strip of bacon, securing the ends of the bacon with a toothpick. Grill, turning occasionally, until bacon is crisp and the corn is fully cooked, 12 to 15 min. Serve with carved chicken.
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