Preheat the oven to 375 degrees 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. Roast chicken uncovered for 45 minutes.
While the chicken is roasting, peel the carrots and potatoes and cut them and the celery into 1-inch pieces. Peel the onions, and cut into wedges.
Remove the chicken from the oven. Spread the carrots, celery, potatoes and onions around the chicken. In a 1-quart saucepan, heat the butter over low heat just 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 until the vegetables are tender when pierced with a fork.
Carve chicken and serve with the vegetables along with a side salad of greens, chopped apple, and vinegar.