Heat olive oil in a skillet over medium heat; saute onion and green bell pepper until tender, 5 to 10 minutes.Advertisement
Mix flour, salt, and pepper together in a gallon-size resealable bag. Cut each pounded chicken breast in half and add to flour mixture; toss to coat.
Place coated chicken into skillet with onion mixture. Cook until chicken is browned, 3 to 4 minutes per side. Drizzle lime juice over chicken mixture.
Stir tomatoes and oregano into chicken mixture, cover skillet with a lid, and cook until tomatoes soften, sauce thickens, and chicken is no longer pink in the center, 5 to 10 minutes. Add water if needed. Top each piece of chicken with a slice of provolone cheese and serve with the tomato sauce.