In large ovenproof skillet heat olive oil over medium heat. Add chicken breast and brown each side; approximately 5 minutes per side. Place on oven proof plate, cover with foil and place in oven for 15-20 minutes or until no longer pink (times varies with the size of the chicken breast).
In same skillet whisk together balsamic vinegar and honey. Bring to boil, reduce heat to low and simmer until reduced to about 1/2 cup; approximately 10 minutes. Place chicken in skillet with balsamic sauce. Top each piece of chicken with one piece of mozzarella. Sprinkle grape tomatoes over the chicken. Place under broiler until cheese is melted; approximately 1-3 minutes. Keep a close eye on it as broilers are unpredictable.
Top with basil ribbons. Spoon balsamic reduction sauce over the chicken and serve.
You can cut two large chicken breasts in half lengthwise if desired reducing the size of the portion and baking time.