Place the potatoes and sliced shallots in a heaving roasting pan or skillet. Drizzle with olive oil, the thyme and season well with salt and freshly ground pepper. Season the chicken thighs on both sides with salt and pepper, then place on top of the potatoes.
Bake for 20 minutes at 450, then reduce heat to 350 and continue to cook for 20 to 30 minutes more, or until the chicken is cooked through.
Serve hot and drizzle the natural juices from the pan around the plate.