Season the chicken with salt and pepper.
In a large skillet over medium heat, add the olive oil. When the oil is shimmering add the chicken to the skillet. Cook until browned on both sides, remove from the pan and set aside.
Add the peppers and prosciutto to the now empty skillet. Cook until browned and the prosciutto is crisp about 5 minutes. Add the garlic and cook 1 minute more.
Add the diced tomatoes (with the juices), chicken broth, and the fresh herbs. Using a wooden spoon, scrape the browned bits from the bottom of the pan. Return the chicken back to the skillet, bring the mixture to a boil, then reduce the heat to a simmer. Cover the skillet and cook until the chicken is cooked through, about 15-20 minutes.
Once cooked through, add the capers and parsley, stir to combine. Serve.