Preparation

• Combine the maple syrup, sage, cinnamon, and red pepper flakes in a 1- to 2-quart saucepan. Warm over medium-low heat to meld the flavors, about 5 minutes.
• In a plastic tub or pot just large enough to submerge the chicken, combine the salt and 3 quarts cool water. Reserve 1/2 cup of the maple syrup mixture for the glaze, and add the rest to the water. Stir until the salt is dissolved, and let cool to room temperature. Add the chicken, breast side down, cover, and refrigerate for 8 to 24 hours.
• Remove the chicken from the brine, and discard the brine. Tie the legs together with twine, fold the wings under the back, and place breast side up on a rack set in a roasting pan. Refrigerate uncovered for 1 hour to allow the skin to dry.
• Position a rack in the center of the oven and heat the oven to 375°F. Meanwhile, remove the chicken from the refrigerator and let it sit at room temperature for 30 minutes.
• Roast for 10 minutes. Reduce the oven temperature to 325°F and roast for another 30 minutes. Put a cup of water in the roasting pan to prevent the syrup from burning, brush the chicken with some of the reserved maple syrup mixture, and return it to the oven, rotating the pan. Continue to roast, brushing with the maple syrup mixture every 15 minutes, until an instant-read thermometer inserted into the thickest part of the thigh reads 165°F, 35 to 45 minutes more. Let rest for 15 minutes before carving and serving.