Preheat the oven to 350°F. Rinse the chicken inside and out with cold water. Pat dry with paper towels. Season the cavity of the chicken with salt and pepper. Squeeze the juice from the lemon and orange halves all over the chicken. Stuff the lemon and orange halves into the cavity, along with the onion, celery and thyme. Place the chicken on a rack in a roasting pan. Drizzle the olive oil over the skin and season with salt and pepper. Roast the chicken in the oven for 1 1/2 hours or until a thermometer inserted into the thickest part of the thigh registers 160°F. Let the chicken rest for 15 minutes. Remove and discard the skin before carving.