In a large, shallow bowl or a 13-by-9-inch baking pan, combine the marinade ingredients.
Place the chicken, breast side down, on a cutting board. Using sturdy kitchen shears or a very sharp knife, cut from the neck to the tail end, along either side of the backbone, to remove it. Take special care if you are using a knife; you’ll be cutting through small bones and will have to use some force.
Once the backbone is out, you’ll be able to see the interior of the chicken. Make a small slit in the cartilage at the bottom end of the breastbone. Then, placing both hands on the rib cage, crack the chicken open like a book. Run your fingers along either side of the cartilage in between the breasts to loosen it from the flesh. Grab the bone and pull up on it to remove it along with the attached cartilage. The chicken should now lie flat.
Place the chicken inside the bowl or in the baking pan and turn to coat it evenly with the marinade. Cover with plastic wrap and refrigerate for about 2 hours.
Prepare the grill for direct cooking over medium-low heat (about 350°F).
Brush the cooking grates clean. Place the chicken, bone side down, over direct medium-low heat and put a cast-iron skillet, or weight a sheet pan down with two foil-wrapped bricks, directly on top. Close the lid and cook for 20 to 30 minutes. Remove the skillet, turn the chicken over, replace the weight, close the lid, and cook until the juices run clear and an instant-read thermometer inserted into the thickest part of the thigh (not touching the bone) registers 160° to 165°F, 20 to 30 minutes. Remove from the grill and let rest for 5 to 10 minutes (the internal temperature will rise 5 to 10 degrees during this time). Serve warm.