Bring one quart of water to a boil in a large saucepan over high heat. Add the remaining brine ingredients to the boiling water and whisk till the salt and sugar have melted. Remove from the heat.
Fill a large pot with four quarts of iced water. Add the brine to the ice water, stirring the brine till the ice melts.
Remove any giblets from inside the chicken, and submerge the chicken completely in the cold brine. Cover and refrigerate, allowing the chicken to brine for six hours, or overnight if possible.
Preheat your oven to 425°F. While the oven is preheating, remove the chicken from the brine, pat it dry with paper towels and remove the spine of the chicken to spatchcock it.
Spray a wire cooking rack with a light coat of nonstick cooking spray, then place the rack in a large cast iron skillet or raised edge baking sheet. Place the spatchcocked chicken on the cooling rack, and evenly coat it with the olive oil.
Place the chicken in the preheated oven. Allow the chicken to roast for 15 minutes. Then, reduce the oven temperature to 350°F. Allow the chicken to continue roasting until the skin is golden brown and the internal temperature in the thigh reaches 155°F is indicated with a reliable quick read thermometer. About 20-25 minutes.
Remove the chicken from the oven, cover with aluminum foil and allow it to rest for 10 minutes. Then carve the chicken and serve hot.