1. Preheat oven to 350°. Season chicken on both sides with salt and pepper. Cook chicken in hot oil in a large ovenproof skillet over medium-high heat 2 minutes on each side or until browned. Remove chicken from skillet, reserving drippings in skillet.
2. Reduce heat to medium. Add shallot to hot drippings in skillet, and sauté 3 minutes or until tender. Add ginger and garlic; sauté 45 to 60 seconds or until fragrant. Add basil, chicken broth, and peaches. Return chicken to skillet, and turn to coat.
3. Bake at 350° for 15 minutes or until chicken is done.