In large skillet over medium heat, add oil, chicken, and Italian seasoning. Cook 5 minutes on each side until fully cooked. Shred chicken and set aside.
Arrange tortillas on counter. Spread each tortilla with 2 tablespoons dressing, 1 cup lettuce, 1/4 cup chicken, and 2 tablespoons cheese.
Wrap tortilla tightly. Serve with additional dressing and cheese, if desired.