Chop and slice all the ingredients for the salad. Neatly stack the ingredients in a large glass bowl in this order: romaine, carrots, radishes, grilled chicken, snow peas, crispy Chinese noodles, red onion, green onion, almonds. If you plan to make the salad early and save for later, keep the crispy Chinese noodles separate and add as the final layer before serving.
To make the Asian salad dressing, place all the ingredients in a small jar. Cover the jar and shake to combine. Refrigerate until ready to serve.