In a large bowl, combine the shredded chicken with the Caesar dressing. Mix well to ensure the chicken is thoroughly coated. Season with salt and pepper to taste.
In another bowl, toss the chopped romaine lettuce and halved cherry tomatoes lightly with a drizzle of olive oil and a pinch of salt.
Heat the corn tortillas in a dry skillet over medium heat for about 30 seconds on each side or until warm and pliable.
To assemble each taco, place a generous scoop of the Caesar chicken mixture in the center of the tortilla.
Top with the dressed romaine and cherry tomato mixture, followed by slices of avocado and a sprinkle of grated Parmesan cheese.
Optionally, garnish with fresh parsley for added color and flavor.