Combine tomato, onion, basil, oil, and 1/2 teaspoon salt in a medium bowl. Let stand at room temperature.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound each piece to 1-inch thickness using a meat mallet or small heavy skillet. Sprinkle both sides of chicken with remaining 1/2 teaspoon salt and pepper.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add 3 chicken breast halves to pan; cook 4 minutes on each side or until chicken is browned and done. Remove from pan; keep warm. Repeat procedure with remaining 3 chicken breast halves.
Stir cheese into tomato mixture. Place 1 chicken breast half on each of 6 plates; top each serving with about 1/3 cup salsa.