Rinse and pat dry the chicken breast halves. Combine the rosemary, garlic, salt and pepper in a small mixing bowl, and mix well.
Place chicken in a large bowl, and drizzle oil over the pieces. Rub with the spice mixture.
Cover and refrigerate the chicken overnight.
Preheat the oven to 450 degrees F. Spray an iron skillet or a heavy roasting pan with a nonstick cooking spray. Place chicken in the pan and bake for 10 minutes. Turn the chicken over. If the drippings begin to stick to the pan, stir in 3 to 4 tablespoons of water.
Bake chicken another 10 minutes. The chicken should be golden brown and no longer pink in the center. If the pan is dry, stir in another 1 to 2 tablespoons of water. This will loosen the drippings.
Drizzle the balsamic vinegar over the chicken while it is in the pan. Transfer the chicken to the plates. After stirring the liquid in the pan, drizzle it over the plated chicken.