Combine balsamic vinegar, soy sauce, shallots, brown sugar, garlic, and 1 tablespoon olive oil. Place chicken in a zip-top plastic bag. Add vinegar mixture; seal. Marinate in refrigerator for 1 hour. Preheat oven to 400°. Remove chicken from bag; reserve marinade. Place marinade in a small, heavy saucepan over medium heat; bring to a boil. Boil 2 minutes or until syrupy, stirring frequently. Remove from heat; divide mixture in half. Heat a large ovenproof skillet over medium-high heat. Add 1 tablespoon olive oil; swirl. Add chicken; sauté 4 minutes. Turn chicken over; brush with half of vinegar mixture. Bake at 400° for 6 minutes or until done. Remove chicken from oven; brush with remaining vinegar mixture.