1. Sprinkle chicken pieces evenly with pepper and salt.
2. Cook chicken in hot vegetable oil in a large skillet or Dutch oven over medium-high heat 10 minutes or until slightly brown on all sides, turning pieces often. Remove chicken from skillet, and drain on paper towels. Drain excess oil from skillet.
3. Add chopped garlic to skillet, and sauté over medium heat 2 minutes. Add tomato paste and 1/2 cup chicken broth, stirring to loosen particles from bottom of skillet. Add 2/3 cup balsamic vinegar and 3 tablespoon honey; increase heat to medium-high, and bring glaze to a boil.
4. Add chicken, reduce heat to medium-low, and cook, uncovered, turning occasionally, 45 minutes to 1 hour or until chicken is done. Spoon balsamic glaze mixture over chicken, and sprinkle evenly with green onions.