Heat oil in a deep-fryer to 350 degrees F (175 degrees C).
In a medium bowl, mix together the shredded chicken, cheese, green salsa, and onion. Spoon about 1 1/2 tablespoons of the mixture onto tortillas, or enough so that when rolled up, each one is about 1 inch wide. Filling should not come to close to the ends, or it will fall out. Secure rolls with toothpicks.
Fry rolls 4 or 5 at a time so there is enough room between them for even cooking. Cook for 3 to 5 minutes, or until golden brown. Once they float, I leave them in for about another minute. If the taquitos are not crisp when cool, you haven't cooked them long enough. Drain on paper towels. Serve with sour cream, salsa and guacamole for dipping.
