In a small bowl, combine the chopped, cooked chicken and buffalo sauce. Stir well until chicken is completely coated. Set aside.
In a separate small bowl, combine the softened cream cheese and ranch dressing. Using a spoon or hand mixer, blend until smooth and creamy.
Lay the tortillas on a flat surface. Divide the cream cheese mixture evenly between them, then add the buffalo chicken, cheeses, and chives. For best results, don't put the ingredients all the way to the edge of the tortillas.
Starting at one end, roll each tortilla tightly into a long tube. (*Note: pinwheels will be full!) Wrap each rolled tortilla in plastic wrap and refrigerate for at least one hour to allow the ingredients to set.
Remove the rolled tortillas from the refrigerator, uncover, and slice into pieces about 1 1/2 inch thick. Transfer to a serving plate and garnish with extra chives as desired.