Combine first 7 ingredients in a small bowl. Add 2 teaspoons oil; toss gently to combine. Let stand 15 minutes.
Brush chicken evenly with remaining 1 tablespoon oil, and sprinkle with 1/4 teaspoon salt and pepper. Place chicken on a grill rack coated with cooking spray; grill 6 minutes on each side or until chicken is done. Remove from grill. Let stand 5 minutes before slicing thinly.
Add cheese and remaining 1/4 teaspoon salt to tomato mixture; stir gently to combine. Arrange sliced chicken evenly on bottom halves of rolls. Top each serving with one-fourth of tomato mixture, and cover with top halves of rolls. Serve immediately.