Heat 1 teaspoon oil in a large nonstick skillet over medium heat. Add mushrooms, minced green onions, and ginger; sauté 3 minutes. Spoon into a small bowl, and stir in 1 tablespoon teriyaki sauce. Set aside.
Cut a horizontal slit through the thickest portion of each chicken breast half to form a pocket. Stuff about 1 1/2 tablespoons of mushroom mixture into each pocket.
Heat 1 teaspoon oil in skillet over medium-high heat. Add chicken; sauté 6 minutes on each side or until chicken is done. Remove chicken from skillet. Set aside; keep warm.
Add 2 tablespoons teriyaki sauce, orange rind, orange juice, sherry, and honey to skillet, and bring to a boil. Cook for 2 minutes or until reduced to 1/4 cup. Spoon orange glaze over chicken, and garnish with sliced green onions, if desired.