Preheat oven to 350 F. Boil 1 cup water in small pan. Add sun-dried tomatoes, remove heat, and cover. Let stand 30 minutes or until soft. Drain and finely chop.
Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add shallots, sugar, and garlic. Cook until lightly browned, stirring often. Spoon shallots into a small bowl and combine with 1½ teaspoons vinegar, chopped tomatoes, shallots, goat cheese, basil, and ¼ teaspoon salt.
Cut a slit into the side of chicken breast to form a pouch for the stuffing. Stuff about 2 tablespoons cheese mixture into each pocket. Sprinkle chicken evenly with ½ teaspoon salt and black pepper.
Heat 1 tablespoon oil in pan over medium heat. Add chicken and cook 6 minutes on each side until brown. Remove from pan and cook on baking sheet in oven for 10 minutes, five on each side, or until cooked through.
In the same pan the chicken was cooked in, add broth, 2 tablespoons vinegar, and thyme and bring to a boil. Dissolve cornstarch in the water, stirring with a fork. Add cornstarch mixture to pan and cook one minute or until sauce thickens, stirring constantly. Serve sauce over chicken.
Adapted from Cooking Light, March 2004
Recipe by Modern Martha at http://modernmartha.com/2011/05/goat-cheese-sun-dried-tomato-stuffed-chicken/