Preheat and prep: Heat your oven to 400°F (200°C). Pat the chicken dry with paper towels and season both sides with salt, pepper, and half the oregano.
Mix the marinade: In a small bowl, stir together olive oil, garlic, lemon zest, lemon juice, thyme, smoked paprika, and red pepper flakes.
Set aside.
Assemble the pan: Add the onion, bell pepper, zucchini, and tomatoes to a large sheet pan or oven-safe skillet. Toss with half the marinade and a pinch of salt. Spread into an even layer.
Nestle the chicken: Place the chicken on top of the vegetables.
Spoon the remaining marinade over the chicken. Scatter olives and capers around the pan. Pour the chicken broth into the pan edges to keep things moist.
Roast: Bake for 20–25 minutes for breasts or 25–30 minutes for thighs, until the chicken reaches an internal temperature of 165°F (74°C) and the veggies are tender.
Optional broil: For light char and extra flavor, broil for 2–3 minutes at the end.
Watch closely to avoid burning.
Finish and serve: Sprinkle with feta and fresh herbs. Taste and adjust with a squeeze more lemon or a pinch of salt. Serve as-is or with a small portion of brown rice, quinoa, or cauliflower rice.