Preheat the oven to 350 degrees F (175 degrees C). Place chicken breasts skin side up in a glass baking dish.
Bake chicken, uncovered, for 35 to 40 minutes in the preheated oven. Remove from the oven, and coat each piece generously with barbeque sauce. Lay 2 folded slices of ham over each breast, and top with slices of cheese.
Return to the oven, and continue baking for 10 to 15 minutes, until cheese is melted. Let stand 5 minutes before serving.
