Take the chicken out of the refrigerator and let stand at room temperature for 1½ to 2 hours, or until it comes to room temperature.
Preheat the oven to 475°
Remove the neck and innards if they are still in the cavity of the chicken. Using a paring knife, cut out the wishbone from the chicken. (Makes it easier to carve the chicken.)
Generously season the cavity of the chicken with salt and pepper, add 3 of the garlic cloves and 5 sprigs of thyme, and massage the inside of the bird to infuse it with the flavors. (Note: I like to add a couple of wedges of onion or lemon into the cavity also.)
Truss the chicken. (Easier than it sounds. Cut a long piece of cooking twine. With the chicken laying breast up, loop the twine under the neck and bring it around both sides of the wings and around the bottom of the drumsticks. Cross the legs over each other and wrap the twine, from opposite sides, around the crossed legs. Tie a knot and trim the ends of the string to about 2 inches.)
Cut off the dark green leaves from the top of the leeks. Trim off and discard any darkened outer layers. Trim the root ends, cutting around them on a 45 degree angle. Slit the leeks lengthwise almost in half, starting ½ inch above the root ends. Rinse the leeks well under warm water.
Cut off both ends of the rutabagas. Stand the rutabagas on end and cut away the skin, working from top to bottom and removing any tough outer layers. Cut into ¾ inch wedges. Repeat with the turnips cutting the wedges to match the size of the rutabagas.
Combine all the vegetables and the remaining garlic cloves and thyme sprig in a large bowl. Toss with ¼ cup of the oil and season with salt and pepper. Spread the vegetables in a large cast iron skillet or a roasting pan.
Rub the remaining oil all over the chicken. Season generously with salt and pepper. (Note: Put the chicken into the same bowl which previously held the veggies. Pour the oil over it and sprinkle with salt and pepper. Now you can turn the chicken over and around inside the bowl—cutting down on the amount of mess on your counter.)
Make a nest in the center of the vegetables and nestle the chicken in it. Cut the butter into 4 or 5 pieces and place over the chicken breast.
Put the chicken in the oven and roast for 25 minutes. Reduce the heat to 400° and roast for an additional 45 minutes, or until the temperature registers 160°F in the meatiest portions of the bird—the thighs, and under the breast where the thigh meets the breast—and the juices run clear. If necessary, return the bird to the oven for more roasting: check it every 5 minutes.
Transfer the chicken to a carving board and let rest for 20 minutes.
Just before serving, set the pan of vegetables over medium heat and reheat the vegetables, turning them and glazing them with the pan juices.
Cut the chicken into serving pieces, arrange over the vegetables, and enjoy!.