In a bowl, combine chicken, carrot and water chestnuts. In another bowl, combine cornstarch, water, soy sauce and ginger until smooth. Add to chicken mixture; toss to coat. Spoon 1 teaspoon of filling in the center of each wonton wrapper. Moisten edges with water. Bring opposite points together; pinch to seal. Place on greased baking sheets. Combine butter and oil; brush over wontons. Bake at 375° for 10-12 minutes or until golden brown. Serve with plum or sweet-sour sauce.
Note: Fill wonton wrappers a few at a time, keeping the others covered with a damp paper towel until ready to use.