Preheat a grill pan over medium heat on the stove top. Spray with cooking spray. Combine balsamic and olive oil in a bowl. Season both sides of chicken with pinches of salt and place on grill. Brush top sides of chicken with balsamic mixture. Cook for 4-5 minutes and flip chicken. Brush with additional balsamic and cook for an additional 4-5 minutes or until cooked through. During the last 2 minutes of grilling place 2 slices of cheese over top each chicken to melt.
In a large bowl combine the tomatoes, basil garlic, salt and balsamic. Toss gently to combine. Place chicken breasts on a serving plate and top with tomato mixture. Serve warm.