For the salad: Using a vegetable peeler, shave the carrot and add to a large salad bowl. Stir in the cabbage, lettuce, pepper, Thai basil, chicken, 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, if using.
Pour the dressing over the salad and toss well. Garnish with the chow mein noodles and serve.
*Cook's Note: can be found in specialty Asian markets
**Cook's Note: To toast the slivered almonds, arrange them in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven for 8 to 10 minutes until lightly golden. Cool completely before using.