Season the chicken pieces with ½ teaspoon salt and ½ teaspoon pepper. Warm the olive oil in a large, heavy skillet over medium heat. Once the oil is hot, add the chicken and sear it on both sides until the exterior turns a rich golden brown. Transfer the browned chicken to a plate and keep it aside.
Using the same skillet, still over medium heat, add the sliced bell peppers and chopped prosciutto. Cook for about 5 minutes, or until the peppers begin to blister and soften and the prosciutto becomes crisp around the edges. Stir in the chopped garlic and cook for another minute, allowing its aroma to release without burning.
Pour in the diced tomatoes, white wine, thyme, and oregano. Use a wooden spoon to scrape up any browned bits from the bottom of the pan—these add essential depth to the sauce. Return the chicken pieces to the skillet, nestling them into the mixture. Add the chicken stock, bring the liquid to a gentle boil, then reduce the heat to low. Cover the pan and let everything simmer for 20 to 30 minutes, until the chicken is fully cooked and tender.
If serving right away, stir in the capers and chopped parsley just before plating. Mix well so the bright flavors disperse through the sauce. Serve warm.
If preparing ahead of time, transfer the chicken and sauce to an airtight container once slightly cooled, then refrigerate. To serve the next day, reheat the dish gently over medium heat until simmering, then finish with the capers and parsley before enjoying.