In a mixing bowl, whisk together Greek yogurt, mayonnaise, and olive oil until smooth. Then, add mashed anchovy fillets, lemon juice, Worcestershire sauce, Dijon mustard, and minced garlic. Season with salt and black pepper to taste, and mix until all ingredients are well combined.

In a large mixing bowl, combine chopped rotisserie chicken, chopped Romaine lettuce, and halved grape tomatoes. Add grated Parmesan cheese and drizzle freshly made Caesar dressing over the mixture. Gently toss everything together until evenly coated.

Carefully fold in diced avocado into the mixture, ensuring not to mash the avocado.

Lay a burrito-sized tortilla flat on a clean surface. Spoon a generous amount of the chicken salad mixture along the center, fold sides inward, then roll tightly from bottom up.

Slice each wrap in half, revealing the colorful filling inside. Arrange the halves on a serving plate and enjoy immediately.