Pat dry and season: Pat the chicken dry with paper towels for better browning. Season all sides generously with salt and pepper.
Brown the chicken: Heat olive oil in a large skillet or Dutch oven over medium-high. Sear chicken skin-side down until deeply golden, 5–7 minutes.
Flip and brown the other side, 3–4 minutes. Transfer to a plate. Do this in batches if needed to avoid overcrowding.
Soften the vegetables: Reduce heat to medium.
Add onion, peppers, and mushrooms with a pinch of salt. Cook, stirring, until softened and lightly browned, about 6–8 minutes.
Add aromatics: Stir in garlic, oregano, thyme, and red pepper flakes. Cook until fragrant, about 30 seconds.
Deglaze with wine: Pour in the red wine, scraping up browned bits.
Let it simmer for 2–3 minutes to reduce by about half.
Build the sauce: Add crushed tomatoes, chicken broth, capers, olives, and bay leaf. Stir and bring to a gentle simmer. Taste and adjust salt if needed.
Nestle in the chicken: Return the chicken and any juices to the pan, skin-side up.
Reduce heat to low so it gently bubbles. Cover and simmer 20 minutes (boneless thighs) to 30–35 minutes (bone-in), until chicken is cooked through and tender.
Uncover to thicken: Remove the lid and simmer another 5–10 minutes to thicken the sauce. If you want a silkier finish, stir in the butter.
Remove the bay leaf.
Taste and finish: Adjust seasoning with salt, pepper, and a pinch of sugar if the tomatoes taste too sharp. Scatter chopped parsley on top.
Serve: Spoon chicken and sauce over pasta, creamy polenta, mashed potatoes, or alongside crusty bread. A simple green salad balances the richness.