Cut chicken into 1-inch pieces. In a food processor, combine the chicken, scallions, soy sauce, ginger, honey, and garlic with on/off turns until finely chopped.
Place 1 tsp. of the filling into the center of each wonton wrapper. Lightly wet the circumference of each wrapper with water so edges will stick together. Fold in half, then pleat the edges so the wontons resemble a slightly fanned-out flower. (Or improvise!)
Steam over boiling water in batches for 8 to 10 minutes.
In a small bowl, combine the soy sauce, stock, and oil. Use as a dipping sauce for the wontons.