Combine the grated cheese and chopped green chiles. Separate wonton wrappers and lay on waxed paper. Lightly beat together the egg white and water in a small bowl. Place one-half teaspoon of the cheese mixture on each wonton wrapper. Tightly fold the wonton like an envelope, sealing the edges with the egg and water wash. When all of the wrappers are filled, fry the wontons, two or three at a time in 2 inches of hot oil, until brown. Drain on paper towels. Frying the wontons should be done quickly since the cheese will begin to ooze from the wrapper if left too long in the oil. If the wontons are not being served immediately, place them in a single layer on a cookie sheet and freeze. Once they are frozen, place the wontons into plastic freezer bags. When ready to serve, reheat for five minutes at 350°. Serve with guacamole slightly thinned with lime juice or cream. Makes 40 appetizers.