In a 10-inch skillet combine apple juice, bouillon granules, garlic, tarragon, and pepper. Bring to boiling. Add chicken breasts; reduce heat. Cover and simmer for 7 minutes.
Turn chicken over; add apple slices and green onions. Cover and simmer 4 to 5 minutes more or until chicken is tender and no longer pink.
With a slotted spoon remove chicken and apples; keep warm. Reserve cooking liquid.
In a small bowl stir together the water and cornstarch. Stir into liquid in skillet. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more. Spoon over chicken and apples. Makes 4 servings.