In a saucepan, bring the vinegar to a boil. Reduce heat, and simmer 15 minutes, stirring frequently, until thickened.
Cut a pocket in each chicken breast. Fill each pocket with an equal amount of mozzarella cheese, and season with salt and pepper. Wrap each chicken breast with a slice of ham. Arrange the wrapped chicken breasts in a baking dish.
Place the tomatoes around the chicken, sprinkle all with olive oil, and season with salt and pepper.
Bake 25 minutes in the preheated oven, or until chicken is no longer pink and juices run clear.
In a saucepan with enough lightly salted water to cover, boil the potatoes 15 minutes, or until tender.
Drain, return to the pan, and coat with the pesto.
Place chicken breasts, tomatoes, and potatoes on serving plates, and drizzle with the reduced balsamic vinegar to serve.
