Make a small hole in the extra skin on the legs and poke the end of the drumstick through to form a perfect package. Toss the chicken generously with olive oil and salt, to taste. Arrange the chicken on a sheet tray or baking dish lined with parchment or silpat. Roast the chicken until it is about 3/4 of the way done, about 20 to 25 minutes. The skin should start to brown and crisp.
While the chicken is roasting, combine the maple syrup and cayenne in a small saucepan over medium heat. Cook until the syrup is reduced by about 1/2 to 3/4 or until the syrup is very thick and syrupy.
After the chicken has roasted for 20 to 25 minutes, brush each piece of chicken generously with the reduced syrup. Continue to roast for another 10 to 12 minutes, brushing the skin with the syrup 1 or 2 more times while cooking. The skin should start to become very dark and sticky. If the skin starts to get too dark, cover it loosely with aluminum foil. Transfer the chicken to a serving platter and let rest about 10 minutes before serving.