1whole chicken3 ½ to 4 pounds, rinsed and patted dry (remove any giblets and save for another use)
Kosher salt and freshly ground pepperto taste
Preheat the oven to 400°F.
Separate the garlic cloves, but do not peel them. In a large bowl combine the garlic, shallots, and potatoes. Drizzle over the olive oil and toss to combine.
Combine 2 tablespoons of the butter, garlic, and rosemary in a small bowl. Carefully loosen the skin of the chicken over the breast area and use your hand to work the butter mixture under the skin and over the meat. Place the lemon halves into the cavity of the chicken. Rub the remaining 2 tablespoons of the butter over the skin of the chicken, and season with salt and pepper.
Place the chicken on a wire rack in a roasting pan. Distribute the potatoes, shallots and garlic around the chicken. Roast for about 50 to 60 minutes, until the skin is browned and crispy and an instant read thermometer registers 165° F when inserted into the meaty part of the thigh, not touching the bone. Or, when you make a small cut in the thigh, the juices should run clear, not pink.
Transfer the chicken to a cutting board and let it sit for 10 to 15 minutes so that they juices settle in the meat. Carve the chicken (discard the lemon inside the chicken), then arrange on a serving platter surrounded by the roasted garlic and shallots and serve hot, warm, or room temperature. The roasted garlic cloves will be soft and mellow in flavor. They are wonderful squeezed out of their paper skins onto toast, bread, or slices of the chicken.