Preheat a large non-stick skillet to medium-high heat. Lightly butter one side of each tortilla with about ½ a teaspoon of butter.
Place one tortilla buttered side down in a hot skillet over medium heat. Layer half of the cheese, the bacon, the chicken chunks, and the remaining cheese on top of the tortilla. Place the second tortilla on top, buttered side up, and cook for a minute or two.
Cover with a lid and add a tablespoon of water to the pan. Allow the steam to melt the cheese, about a minute.
When the cheese is melting and the tortilla facing the skillet begins to brown, use a large spatula to carefully flip the tortilla over and cook on the second side for a few minutes.
When everything has melted together and the tortillas are golden and crisp, remove the quesadilla from the skillet and slice it into wedges. Serve warm with plenty of ranch dressing for dipping.