Heat the oven to 375°F. Fold the wings of the chicken across the back so tips are touching. There may be a little resistance, but once they are in this position, they will stay. Tie the legs to the tail with string or use skewers; if the tail is missing, tie the legs together.
In a shallow roasting pan, place the chicken with the breast side up. Insert an ovenproof meat thermometer so the tip is in the thickest part of inside thigh and does not touch bone. Roast chicken uncovered 45 minutes.
While the chicken is roasting, peel the carrots, and cut into 1-inch pieces. Cut the celery into 1-inch pieces. Scrub the potatoes thoroughly with a vegetable brush or peel the potatoes, and cut into 1 1/2-inch pieces. Peel the onions, and cut into wedges.
Remove the chicken from the oven. Arrange the carrots, celery, potatoes and onions around the chicken. In a 1-quart saucepan, heat the butter over low heat just until melted. (Or place the butter in a small microwavable bowl; cover with a microwavable paper towel and microwave on High 10 to 20 seconds or until melted.) Stir the thyme into the butter, then drizzle over the chicken and vegetables.
Cover the chicken and vegetables with foil; roast 45 to 60 minutes longer or until the thermometer reads 180°F and vegetables are tender when pierced with a fork. Or check for doneness by wiggling the legs; if they move easily, the chicken is done.
Remove the vegetables from the pan, and cover with foil to keep warm while carving the chicken.
Place chicken, breast up and with its legs to your right if you're right-handed or to the left if left-handed, on cutting board. Remove ties from legs.