1. Combine the mayonnaise, vinegar, chili powder, garlic, 1 teaspoon salt, and pepper to taste in a mixing bowl. Stir well.
2. Add the chicken, apples, celery, and walnuts and toss the ingredients together to combine. Adjust the seasoning.
3. Set some lettuce leaves on each dinner plate and top with the salad; garnish with the grated cheese.