Preheat oven to 400 degrees. Crumble ramen into small pieces and place on baking sheet along with almonds, spread into an even layer. Bake in preheated oven until golden, tossing once halfway through baking, about 6 - 8 minutes.
Whisk together all of the dressing ingredients until well blended, season with salt to taste, set aside.
To a large bowl add green cabbage, purple cabbage, carrots, green onions, chicken, toasted ramen and almonds and sesame seeds. Drizzle dressing over top and toss to evenly coat. Serve immediately.