In a large, ovenproof skillet or frying pan, mix together the carrots, squash, and broccoli, and coat with the oil. Spread the veggies into 1 even layer.
Place the chicken on top of the veggies.
Season the bird on all sides and in the cavity with salt, pepper, and fresh thyme leaves. While seasoning the bird, make sure that enough seasoning has fallen onto the veggies below to give them good flavor.
To truss the chicken, fold the wingtips underneath the breasts so that they fit snugly. Using a piece of butcher’s twine, tie the legs together so the bird holds a nice shape.
Bake for 1 hour, or until a thermometer inserted into the thickest part of the breast reads 160°F (70°C).
NOTE: Once resting out of the oven, the temperature will continue to rise to a safe 165°F (75°C).
Let the chicken rest for at least 15 minutes once out of the oven, so that all of the juices in the meat can settle and the internal temperature has time to finish rising.
Carve the bird as desired.
Serve on a plate with the veggies, and fresh thyme sprigs for garnish.