Preheat the Oven: Preheat your oven to 400°F (200°C).
Season and Sear the Chicken: Pat the chicken thighs dry and season generously on all sides with salt and pepper. In a large oven-safe skillet or Dutch oven (at least 12 inches), heat the olive oil over medium-low heat. Add the chicken thighs, skin side down, and cook for 8-10 minutes without moving them, allowing the skin to brown and crisp.
Prepare the Vegetables and Add to Skillet: While the chicken is cooking, prepare the shallots, garlic, tomatoes, olives, lemon, capers, and thyme. Once the chicken has browned on one side, flip the thighs over. Be gentle, using a thin spatula to help release the skin if needed. Sprinkle the chicken with Herbes de Provence, then add the shallots, garlic, cherry tomatoes, green olives, lemon wedges, capers, and thyme to the skillet. Pour 1 cup of chicken broth around the chicken, ensuring the ingredients are evenly distributed.
Braise in the Oven: Transfer the skillet to the preheated oven and braise the chicken uncovered for about 1 hour. The chicken is done when it is opaque and reaches an internal temperature of at least 165°F (74°C).
Cool and Serve: Once the chicken is cooked through, remove the skillet from the oven and let it rest for 5 minutes. Serve the chicken with rice or a crusty baguette to soak up the flavorful sauce.