Pat the chicken dry with paper towels. Rub the chicken with 1 tablespoon of the oil and season with 1 1/2 teaspoons of the salt and 1/4 teaspoon of the pepper. Place in a roasting pan or baking dish.
In a small bowl, combine the peaches, shallots, vinegar, thyme, and the remaining oil, salt, and pepper.
Scatter the peach mixture around the chicken. Roast until the chicken is cooked through and a thigh registers 180° F on a meat thermometer, about 1 hour, 10 minutes. Let rest for 10 minutes before carving. Serve with the peaches and pan sauce.