In deep fryer, heavy saucepan or wok, heat 2 to 3 inches of oil to 375°F.
Meanwhile, in food processor bowl with metal blade, combine shrimp, water chestnuts, cornstarch, onions, sherry, gingerroot and salt, process until finely chopped. Add egg; process until combined.
Drop shrimp mixture by teaspoonfuls into hot oil (375°F.). Fry 3 to 4 minutes or until shrimp turn pink and balls are deep golden brown. Drain on paper towels. Serve warm with a variety of dipping sauces.