In a large bowl, toss chicken, coleslaw mix, and drained chow mein vegetables until well mixed. Toss chicken mixture with enough dressing to coat well. Line individual bowls or plates with a small amount of green salad. Spoon chicken mixture on top of green salad. Garnish with noodles and orange segments before serving.
In a small bowl, whisk mayonnaise, soy sauce, and ginger until blended. Set aside, or refrigerate, if not using soon. Whisk again after refrigerating.