Preheat oven to 425º. Remove bag of giblets and rinse chicken, inside and out, removing any excess fat. Drain well and pat dry. Season the cavity generously with salt and pepper, and tuck wings underneath the body. Stuff the chicken with the lemon halves, garlic and a good bunch of fresh thyme sprigs. Next, brush the melted butter all over the chicken, generously salt and pepper, and then tie the legs together with kitchen string.
Place all of the vegetables evenly in the bottom of a large roasting pan. Drizzle with olive oil, season with salt and pepper, and with cleans hands, toss to coat vegetables. Toss in a few more thyme sprigs.
Place chicken over top of vegetables, and roast for 1½ hours, or until juices run clear at the thigh. I added some stock to the pan after about 45 minutes, and then again in another half hour, about a cup or so. I wanted pan juices and it seemed like I wouldn't have enough.
Remove chicken to cutting board, tent with foil and let rest. Remove vegetables to a bowl, leaving drippings behind. Pour drippings into a fat separator, or bowl, and remove fat. Put pan juices in a small bowl or gravy boat and keep warm.
Carve up chicken onto a platter, serve with root vegetables and pan juices. Enjoy.