1. Chop the raw chicken breasts into very fine pieces and place in a medium bowl.
2. Add green onions, ginger, sugar, cornstarch, soy sauce,salt, pepper and oil. Marinate for at least 1/2 hour.
3. Place the broth ingredients in a large pot (dutch oven) and bring to simmer.
4. Fill the won ton wrappers by placing about 1/2 teaspoon of filling into the center of each wrapper, moisten edges with water or egg white and fold into a triangle. Press edges to seal.
5. Using a dutch oven, or large pot, bring about 8 cups of water to a boil.
6. Drop the won tons into the boiling water a few at a time so that they are not over crowded (maybe 10 - 12 won tons) and let cook for about 5 - 7 minutes. They will float to the top as they cook.
7. Remove from boiling water with slotted spoon and place the won tons directly into the broth.
8. Simmer 10-15 minutes longer, then serve.