Prepare a pasta of your choice, according to the instructions on the package if you decide to serve this dish with pasta.
Season the chicken breasts with salt and pepper. Heat oil and butter in a heavy-bottom skillet or cast iron skillet. Add the chicken breasts and sauté over medium-high heat, for about 5 minutes on each side, turning over once the chicken is browned, and transfer to a plate.
Reduce heat, and add garlic, and shallots and sauté for about a minute. Then add peppers and sauté for a couple of minutes. Add the tomato sauce, tomato paste, and cook for 15 minutes. The last 5-7 minutes return chicken to the skillet and add the fresh oregano and basil.
Grate Parmesan cheese over the chicken, and garnish with fresh parsley and basil.
Serve on it's own or with pasta.