In a large bowl, combine the ground chicken, minced garlic, ginger, scallions, soy sauce, sesame oil and 1/4 teaspoon pepper.
Spoon a heaping teaspoon of the mixture into the center of each wonton wrapper. Wet the edges using your finger dipped in water then fold the wontons in half to form triangles. Bring the two ends of the wontons together so that the tips are touching and seal them with water, pressing them lightly together.
Bring a large pot of water to a boil. Add the wontons and cook until the wonton wrapper is translucent and the chicken is no longer pink and cooked through, 4 to 5 minutes.
Using a slotted spoon, remove the wontons and transfer them to a serving bowl then make the sauce.