Preheat the oven to 400 degrees. In a roasting pan, toss the vegetables with 3 tbsp. oil and 3/4 tsp. thyme; season with salt and pepper. Top the vegetables with the chicken, breast side up. Drizzle the chicken with the remaining 1 tbsp. oil and sprinkle it with the remaining 3/4 tsp. thyme; season.
Roast, stirring the vegetables occasionally, until they are tender and an instant-read thermometer inserted in the thickest part of the chicken thigh registers 165 degrees, about 1 hour 45 minutes. Let the chicken rest in the pan 15 minutes.
Tilt the chicken and pour the juices from the cavity over the vegetables. Transfer the chicken to a cutting board. Cut off the wings and legs, then cut the drumsticks from the thighs and cut the breasts from the bones.
Reserve half the chicken and half the vegetables for the Creamy Chicken & Biscuits. Divide the rest among plates; squeeze oranges over the chicken.