Shred the cooked chicken into bite-sized pieces and set aside in a large mixing bowl.
In the same mixing bowl, add mozzarella cheese, cream cheese, Parmesan cheese, minced garlic, Italian seasoning, salt, black pepper, and chopped parsley. Mix until well combined.
Take a large lettuce leaf and lay it flat. Spoon a generous amount of the cheesy chicken mixture into the center, fold the sides over, and roll it up tightly.
Heat olive oil in a skillet over medium heat. Place the assembled wraps seam-side down in the skillet and cook for 2-3 minutes on each side until the lettuce is slightly wilted and the filling is heated through.