Heat the olive oil in a large skillet over medium-high heat. Once hot, add the onion and sauté until it starts to soften, about 3–4 minutes.
Tuck in the garlic and cook for another 30 seconds, until fragrant. Move quickly to prevent it from browning too much.
Season the chicken thighs with salt and pepper. Place them skin-side down in the skillet and sear until the skin is golden and crisp, about 5–6 minutes per side. You don’t need to cook them through yet; the goal is color and flavor.
Remove the chicken and set aside. Add the halved tomatoes to the pan, tossing them in the rendered fat for a minute or two until they begin to release their juices.
Return the chicken to the pan, skin-side up. Add olives, capers (if using), oregano, thyme, red pepper flakes, and lemon zest. Pour in the broth and bring the mixture to a gentle simmer.
Reduce heat to medium-low, cover, and simmer for about 15–20 minutes, or until the chicken is cooked through and tender and the sauce has thickened slightly.
Stir in lemon juice and adjust salt and pepper to taste. If you like a brighter finish, sprinkle with fresh parsley just before serving.
Serve the dish directly from the skillet with crusty bread or over rice or quinoa to soak up the sauce. A simple green salad on the side rounds out the meal.