Thaw shrimp, if frozen. Rinse shrimp; pat dry with paper towels.
In a 2-quart microwave-safe casserole, combine onion and oil. Cover and microwave on 100% power (high) for 2 minutes. Add shrimp; cover and cook on high for 2 to 3 minutes more or until shrimp turn opaque, stirring once. Drain shrimp and onion in a colander; set aside.
In the same casserole, combine brown sugar, cornstarch, ginger, and black pepper. Stir in undrained pineapple, soy sauce, and vinegar. Cook, uncovered, on high for 5 to 6 minutes or until thickened and bubbly, stirring after every minute.
Stir in sweet pepper. Cook, uncovered, on high for 1 minute. Stir in shrimp mixture and water chestnuts. Cook, uncovered, on high for 30 to 45 seconds more or until heated through, stirring once. Serve with hot cooked rice.