Cut 1 carambola in half crosswise, and squeeze 2 tablespoons juice, using a citrus reamer or juicer; set juice aside. Dice carambola halves; set aside. Slice remaining 3 carambolas crosswise, and set aside.
Combine 2 tablespoons carambola juice, chicken, sherry, brown sugar, gingerroot, soy sauce, and garlic in a bowl, and stir well. Cover and chill 30 minutes.
Drain chicken, reserving marinade. Sprinkle chicken with cornstarch; toss well to coat.
Heat vegetable oil in a large non-stick skillet over medium-high heat. Add chicken and carambola; stir-fry 1 minute. Add bell pepper and onion, and stir-fry 3 minutes or until chicken is done. Add reserved marinade, sesame oil, salt, and pepper; stir-fry 1 minute. Serve over rice.