Use a large, heavy, lidded casserole pan or skillet on medium heat and add the olive oil. Salt and pepper both sides of the chicken and brown each side, 3 to 4 minutes per side. Remove the breasts to a plate.
Next add the bacon pieces to the skillet and cook until browned, 5 minutes. Add the bell pepper and lightly salt and pepper. Cook 4 minutes to soften then add the minced garlic and cook for 30 seconds.
Stir in the white wine and the diced tomatoes and use a wooden spoon to scrape up the browned bits from the skillet and bring to a boil. Add the thyme and oregano and cook for 3 or 4 minutes.
Add the chicken broth and place the chicken breasts back in the skillet. Bring to a simmer and cover to completely cook the chicken, 20 to 30 minutes. Check the temperature of the breasts using an instant read thermometer. (FDA recommends 165° internal temperature. For chicken breasts I prefer 145° to keep them tender.)
While the chicken simmers, cook the white rice according to package directions and keep warm.
Remove the skillet from the heat and stir in the capers and sprinkle with chopped parsley. Taste and adjust salt and pepper seasoning. Serve hot over rice.