For the vinaigrette, combine the shallots, lime juice, cilantro and garlic in a bowl and mix well. Whisk in the oil gradually. Season with salt and pepper. You may prepare up to 1 day in advance and store, covered, in the refrigerator. Bring to room temperature before serving.
For the salad, combine the lettuce, cabbage, chicken, tomatoes, bell peppers, avocado, tortilla chips, corn, pumpkin seeds and onion in a bowl and toss to mix. Drizzle with the vinaigrette and mix well. Sprinkle with the cheese.