Prepare the Chicken : Pat the chicken pieces dry and season generously with salt and black pepper.
Sear the Chicken : Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the chicken pieces, skin-side down, and sear for 4-5 minutes on each side, or until golden brown. Remove from the pan and set aside.
Cook the Vegetables : In the same pan, add the chopped onion, red and yellow bell peppers, and garlic. Sauté for 4-5 minutes, stirring occasionally, until the vegetables soften and become fragrant.
Deglaze the Pan : Pour in the white wine (or chicken broth) and scrape up any browned bits from the bottom of the pan. Let it simmer for 2-3 minutes to reduce slightly.
Build the Sauce : Stir in the crushed tomatoes, tomato paste, chicken broth, dried oregano, dried basil, and red pepper flakes (if using). Mix well to combine.
Add the Chicken and Simmer : Return the seared chicken pieces to the pan, nestling them into the sauce. Cover and reduce the heat to low. Let it simmer gently for 30-35 minutes, or until the chicken is cooked through and tender.
Add the Finishing Touches : Stir in the olives and capers during the last 5 minutes of cooking. Taste and adjust the seasoning with salt and pepper as needed.
Garnish and Serve : Sprinkle the dish with freshly chopped parsley before serving. Enjoy with pasta, rice, or crusty bread to soak up the delicious sauce.