Grill your pineapple by cutting it into slices, sticking it on skewers and grilling over low heat. Cut into smaller, bite sized pieces and set aside.
Sprinkle chicken breasts with salt and pepper and place on a grill or pan on medium heat. Grill or cook on both sides until done, brushing with barbecue sauce. Remove from heat and cut into thin strips or small pieces and set aside.
Warm griddle over medium heat and spray with nonstick cooking spray. Place tortillas on griddle, sprinkle on shredded cheese (½ cup per quesadilla), chicken, pineapple and jalapeno slices.
Top with a small drizzle of barbecue sauce and place another tortilla on top. Flip halfway through cooking. Cook until cheese is melted and quesadillas are golden brown and warmed through.
Notes
If you want to bump up the flavor even more for this dish, feel free to add even more to chicken mixture to make the ultimate bbq chicken quesadillas. Think about adding some black beans, fresh cilantro, southwest spice blend, and red onion.