Pat chicken dry and trim of any excess fat. Sprinkle with 2 teaspoons salt and 1/4 teaspoon of pepper including tossing some in the internal cavity. Put a quartered lemon in the cavity, if desired. Truss the turkey if desired.
In a large bowl, add the squash cubes, Brussels sprouts and shallots. Toss with 1-2 tablespoons olive oil and sprinkle with 3/4 teaspoon salt.
Place the silicone roasting racks on your sheet pan then place the chicken on the racks. Arrange the vegetables around the chicken, in one layer. If your pan is overcrowded, you can place some of the vegetables in the slots of the roasting rack.
Preheat oven to 475 degrees. Check the vegetables after 30 minutes and remove to serving dish when tender. Continue roasting chicken.
Roast chicken until internal temperature reaches 160 degrees in the thigh (45 minutes to 1 hour).
Remove from oven and sprinkle with thyme. Let rest 15 minutes before carving. Cover with foil to keep warm as it rests.