1. Heat a large skillet over medium heat. Add oil to pan; swirl to coat. Add bell peppers; cook 3 minutes, stirring occasionally. Add onion and garlic; cook 10 minutes, stirring occasionally. Add tomatoes; cook 1 minute or until tomatoes wilt. Remove from heat; stir in basil, vinegar, and 1/4 teaspoon salt.
2. While pepper mixture cooks, cut each breast half in half horizontally to form 4 cutlets. Cover cutlets with plastic wrap; pound to 1/3-inch thickness with a meat mallet or small heavy skillet. Discard plastic wrap; sprinkle chicken evenly with remaining 1/2 teaspoon salt and black pepper. Dredge in flour; shake off excess. Melt butter in a large skillet over medium-high heat. Add chicken; cook 2 minutes on each side or until golden and done. Serve chicken with bell pepper mixture.