In a medium bowl combine garlic, balsamic vinegar, and brown sugar. Mix well and set aside.
Preheat the oven to 350 degrees F. Cut a pocket that is about ¾ of the way through each chicken breast, being careful not to cut all the way through.
Season the chicken on both sides with salt, pepper, oregano, and basil. Pour 1 teaspoon of sundried tomato oil over each chicken breast, rubbing some of the seasonings inside the pockets.
Fill each chicken breast with 2 slices of fresh tomato, 2 teaspoons of sundried tomato strips, one slice of mozzarella cheese and 4 fresh basil leaves. Seal with 4 toothpicks diagonally to keep the filling from coming out while cooking.
Heat 2 teaspoons of sundried tomato oil (or olive oil) in a large skillet over medium-high heat. Add the chicken and fry for 2 minutes on each side until golden. Pour the balsamic vinegar mixture into the pan around the chicken and bring to a simmer while stirring occasionally, until the glaze has slightly thickened (about 2-3 minutes).
Transfer to a baking sheet and place into the oven and continue to cook for 10-15 minutes or until the chicken is cooked through and the cheese has melted.
Remove the toothpicks and drizzle with pan juices.