Preheat the oven to 375 degrees. Place chicken breasts between two pieces of plastic wrap and pound to flatten slightly.
Place bread in a food processor and process to crumbs. Add parsley, salt and pepper and process to mix. Transfer the crumbs to a shallow dish.
In a second shallow dish, lightly beat egg whites with a fork. Dip chicken breasts in egg whites, then roll in breadcrumbs.
Spray a large ovenproof skillet with cooking spray and place over medium heat. Carefully add the prepared breasts and cook until browned on one side, about 2 minutes. Turn the breasts over and transfer the skillet to the oven. Bake until no longer pink on the inside, about 15 minutes.
While the chicken is baking, prepare the tomato/basil sauce.
Add tomatoes and balsamic vinegar and cook, shaking the pan, for 2 to 3 minutes, just long enough to heat tomatoes. Stir in basil and remove from the heat. Season with salt and pepper.
Serve the chicken with tomato sauce alongside.