In a medium size bowl, toss the chopped chicken with BBQ sauce. Place one tortilla in a hot skillet over medium-high heat. Layer half of the cheese, the shredded chicken, and the remaining cheese on top of the tortilla. Place the second tortilla on top and cook for a minute or two.
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.