Using a vegetable peeler, shave the carrots into long, thin ribbons. In a large bowl, combine the carrots, spinach, onion, sesame seeds, and chicken. In a separate bowl, whisk together the ginger, soy sauce, vinegar, and oil. Pour the dressing over the salad, toss, and serve.
Tip: Toast sesame seeds in a dry pan over medium heat, shaking the pan constantly for 1 to 2 minutes. Watch them carefully as they burn easily.