Mix chicken, carrots, broth, gingerroot, brown sugar, soy sauce, allspice and pepper sauce in a crockpot. Cover and cook on low heat setting for 7 to 8 hours or until vegetables are tender and chicken is no longer pink in the center. Mix cornstarch and reserved pineapple juice; gradually stir into chicken mixture. Stir in pineapple and bell pepper. Cover and cook on high heat setting for about 15 minutes (I put in the green pepper about 45 minutes before the stew is done.) or until slightly thickened and bubbly. Serve with rice.