Combine first 7 ingredients in a large zip-top plastic bag; seal bag, and marinate chicken breast halves in refrigerator for 1 to 2 hours. Remove chicken from bag, reserving marinade.
Heat oil in a large nonstick skillet over medium-high heat. Add the chicken, and sauté 3 minutes on each side. Remove from skillet. Set aside; keep warm. Reduce heat to medium. Add shallots; sauté 3 minutes. Add reserved marinade and broth to skillet; simmer 3 minutes. Return chicken to skillet, and cook 2 minutes or until thoroughly heated.