Spray an unheated large skillet with nonstick coating. Preheat over medium heat. Add chicken. Cook for 8 to 10 minutes or until tender and no longer pink, turning to brown evenly. Remove from skillet; keep warm.
If desired, remove strips of peel from lime, using a vegetable peeler. Cut peel into very thin strips; set aside. Squeeze 1 tablespoon juice from lime.
In a small mixing bowl combine the 1 tablespoon lime juice, the apple juice or cider, cornstarch, and bouillon granules; carefully add to skillet. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more.
To serve, cut each chicken breast half diagonally into 1-inch-thick pieces; arrange on top of rice. Spoon some of the sauce over each serving. If desired, garnish with lime strips and lime slices. Pass the remaining sauce. Makes 4 servings.