How to Make It
Preheat the oven to 450°. Brush a large heavy rimmed baking sheet with some of the pure olive oil and arrange the potatoes on it in a single layer. Season the potatoes with salt and pepper, drizzle with the remaining pure olive oil and dot evenly with the butter. Bake in the middle of the oven for about 30 minutes, or until tender. Remove the baking sheet from the oven and turn the potatoes. Season them with salt and pepper and sprinkle with the garlic and thyme.
Preheat the broiler. Broil the potatoes about 8 inches from the heat for about 10 minutes, or until browned; do not let the garlic burn. using a spatula, transfer the potatoes to a rack.
Carefully position 1 rack in the upper third of the oven and another in the bottom third. Reduce the oven temperature to 400°. Heat 1 tablespoon of the extra-virgin olive oil in each of 2 large skillets. Season the chicken breasts with salt and pepper. Add the chicken to the skillets, skin side down, and cook over moderately high heat until the skin is golden, about 5 minutes. Turn and cook for 1 minute. Transfer the chicken, skin side up, to a baking sheet.
Arrange the potatoes on a baking sheet and set it on the lower rack in the oven. Set the chicken on the upper rack. Roast for 15 minutes, or until the chicken is cooked through and the potatoes are nicely crisped. Arrange the roasted chicken and potatoes on warmed plates and serve.