A few good recipes for oven-cooked chicken using balsamic vinegar are Roasted Chicken with Balsamic Vinaigrette, Chicken Breasts with Balsamic and Balsamic Glazed Chicken and Roasted Potatoes.
For the first recipe, whisk together 2 tablespoons of Dijon mustard, 2 tablespoons of lemon juice, 2 chopped garlic cloves and some salt and pepper in a bowl. Pour into a resealable bag with one whole separated chicken and allow to marinate for several hours. Bake the chicken in a 400 degree Fahrenheit oven for about one hour. Finish chicken with pan drippings, lemon zest and chopped parsley leaves.
For the second, the chicken is also marinated before cooking. To make the marinade, combine 1/3 cup of balsamic vinegar, 1/4 cup of extra virgin olive oil, 2 teaspoons of minced garlic, and 1 teaspoon each of dried basil, dried oregano and dried thyme. After marinating for at least one hour, arrange the chicken on a foil-lined baking dish and broil in the oven for 10 to 16 minutes or until cooked through, turning once.
To make the last recipe, mix 2 tablespoons of extra virgin olive oil, 3 tablespoons of balsamic vinegar, 1 teaspoon of Dijon mustard and 2 teaspoons of Italian seasoning. Use this mixture to marinate 1 pound of boneless, skinless chicken breast and 1 pound of cut red potatoes. Spray a 9 X 13 inch baking dish with cooking spray, then add the chicken, potatoes and marinade. Arrange the potatoes around the sides of the chicken, and cover and bake at 375 degrees Fahrenheit for 15 minutes. Stir the potatoes and continue to bake for another 20-25 minutes until the potatoes are tender and the chicken is cooked through.