In a medium bowl, combine ground chicken, green onions, garlic, ginger, salt, and pepper. Mix just until combined.
Heat a large nonstick skillet over medium heat. Spray with nonstick cooking spray.
Shape the mixture into 12 evenly sized meatballs. Place them in the skillet, spacing them slightly apart.
Lay one wonton wrapper over each meatball. Lightly press so it rests on top of the chicken.
Pour 1/2 cup water into the bottom of the pan (around the meatballs, not over the tops).
Cover with a tight-fitting lid and cook over medium heat for 7 minutes, or until the chicken reaches an internal temperature of 165 degrees F. and the wrappers are soft and tender.
While the dumplings cook, whisk together soy sauce, rice vinegar, and sesame oil.
Drizzle sauce over the dumplings or serve on the side for dipping. Garnish with extra green onions if desired.