Heat the oil in a large skillet or Dutch oven to medium heat. Pat the chicken dry and season with salt and pepper to taste. Sear the chicken, skin sides down, for 5 minutes or until the skins brown and crisp up. Flip the chicken and cook another 3-4 minutes. Remove the chicken to a plate and set aside. Drain off excess fat.
Return the pan to medium heat and add the onion, peppers, and mushrooms. Saute for 5 minutes to soften slightly.
Add the garlic and cook for 1 minute, or until the garlic becomes fragrant.
Add the wine and bring to a boil. Cook 2-3 minutes, or until the liquid reduces by half.
Add the tomatoes, oregano, chili flakes, and olives. Bring to a boil.
Tuck the browned chicken pieces into the sauce, skin side up, then adjust the heat for a gentle boil. The sauce should just cover the chicken. Add a bit of water or chicken stock if needed.
Cover and cook 30 minutes, or until the chicken is cooked through. You can simmer longer to develop more flavor.
Garnish and serve.