Drain pineapple chunks; save syrup. Brown chicken in a skillet using shortening. Pour off fat; add pineapple syrup, broth, vinegar, sugar, soy sauce and garlic. Cover; cook over low heat 40 minutes. Add green pepper and pineapple. Cook about 10 minutes longer.
Remove chicken from skillet. Combine cornstarch and water; stir into sauce until thickening occurs. Return chicken to skillet. Serve with rice.