1. Clean the grill grates and rub with a little oil. Preheat to 400°F. 

2. Once the grill reaches temperature, set up three cooking zones: Turn off zone one for indirect heat, set zone two on low, and maintain zone three on medium-high heat. If your grill does not have three zones, you need one area for indirect heat and the ability to adjust the heat source so that the grill temperature is maintained between 350⁰ and 400⁰ F for the entire cooking time. 

3. Wash the potatoes, stab each 1-2 times with a sharp knife, and optionally wrap in aluminum foil (potatoes will bake fine on the grill without aluminum foil). 

4. Prepare the chicken by removing the wrapping and the giblet bag from the cavity. Pat the chicken dry and place on a cutting board breast-side down. Cut along the right of the backbone from the tail to the neck. Do the same on the left side and remove the backbone. Lay the chicken open and press down on the wings to break the breastbone so it will lay flat. 

5. Rub all sides with approximately 2 tablespoons olive oil. Liberally season all sides with salt and pepper. 

6. Place the potatoes on the grill over the medium-high heat zone. Lay the chicken flat on the grill over indirect heat, breast-side down. Note: Cooking the chicken over indirect heat will prevent the skin from burning and reduce the dripping enough so that a drip pan is not required. Close the lid and let the chicken and potatoes cook, without opening the lid, for 30 minutes. 

7. Prepare the zucchini quarters for the grill by drizzling approximately 2 tablespoons olive oil over both sides of the zucchini and season to taste with salt and pepper. Set aside until ready to grill. 

8. After the chicken and potatoes have cooked for 30 minutes, turn the chicken to cook the other side. Turn the potatoes or move to the low-heat zone if they are starting to soften. Close the lid and cook for another 30 minutes. 

9. If using BBQ sauce, use a basting brush to coat the chicken after the chicken has cooked for 45-50 minutes. Allow the chicken to cook for 5-6 minutes with the grill lid closed, then gently turn the chicken over to coat the other side with the sauce. Close the lid and cook for another 5-10 minutes. 

10. After one hour of cooking, check the chicken for doneness with an instant-read thermometer. The breast should be 165° F and the thighs and legs should be between 185° and 190° F. If you don’t have an instant-read thermometer, transfer the chicken to a cutting board and slice the skin between the drumstick and the body; when the juices run clear the chicken is done (check both sides to ensure the chicken cooked evenly). If the chicken is not quite done, place back on the grill and check again in 10 minutes. 

11. Remove the potatoes and place the zucchini over the medium-high heat zone. Cook for 3-4 minutes on each side, or until done to your liking. Once done, transfer the zucchini to a serving platter. In preparation for serving, drizzle with balsamic vinegar if desired.

12. While the zucchini cooks, prepare the potatoes by unwrapping the foil, if using, and cutting in half lengthwise. Loosen the flesh with a knife, add butter, and season with salt and pepper. Wrap back up to let the butter melt until ready to serve.  

13. Carve the chicken and serve with the baked potatoes and grilled zucchini.