Soak mushrooms in hot water about 20 minutes or until soft; drain. Rinse in warm water; drain. Squeeze out excess moisture. Remove and discard stems; cut caps into 1/4-inch pieces.
Remove bones and skin from chicken; cut chicken into 1/2-inch pieces. Toss chicken, cornstarch and 1/2 teaspoon salt in medium bowl. Cover and refrigerate 20 minutes.
Remove rind, seeds and fibers from melon. Cut melon into 1/2-inch pieces. Cut ham and bamboo shoots into 1/2-inch pieces.
Heat broth to boiling in 3-quart saucepan. Add mushrooms, melon and bamboo shoots; heat to boiling. Stir in chicken and ham. Heat to boiling; reduce heat. Cover and simmer 10 minutes. Stir in 1 teaspoon salt and the white pepper.