For the salad: Using a vegetable peeler, shave the carrot and add to a large salad bowl. Stir in the cabbage, lettuce, celery, Thai basil (if available), chicken, mandarin oranges, almonds, and sesame seeds.
For the dressing: In a small bowl, whisk together the oil, soy sauce, vinegar, and sugar until smooth. Season with salt and pepper, to taste
Pour the dressing over the salad and toss well. Garnish with the chow mein noodles and serve.