Place the shredded chicken meat, Napa cabbage, radicchio, grated carrots, sliced green onions and chopped peanuts in a large mixing bowl.
Combine all the ingredients for the vinaigrette in a separate bowl or measuring cup and whisk until well combined. Pour over the salad and then toss well, preferably with your hands, to gently massage and bruise the ingredients as you mix.
Serve immediately, or refrigerate for about an hour to allow flavors to meld.
Leftovers will keep well for up to a couple of days in the refrigerator.