Preheat oven to 400 F.
In small bowl, whisk olive oil, basil, garlic, salt, pepper and oregano until combined. Combine 2 tablespoons oil mixture and chicken in resealable plastic bag. Let stand 5-10 minutes at room temperature to marinate.
In medium skillet, heat 2 tablespoons oil mixture over medium heat. Add onions; cook 3-4 minutes, or until crisp-tender. Stir in marinara sauce. Pour mixture into lightly greased 13-by-9-inch baking dish. Arrange chicken breasts in dish, overlapping if necessary. Top with grape tomatoes and cherry tomato stems. Spoon remaining oil mixture over tomatoes.
Bake, covered, 25 minutes, or until chicken is done (165 F) and tomatoes start to burst. Sprinkle with Parmesan, drizzle with balsamic glaze and garnish with fresh basil leaves before serving.