Mix chicken, carrots, broth, ginger root, brown sugar, soy sauce, allspice and pepper sauce in 1 1/2- to 4-quart crock pot slow cooker. Cover and cook on low heat setting 7 to 8 hours or until vegetables are tender and chicken is no longer pink in 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 about 15 minutes longer or until slightly thickened and bubbly.
