Put the chicken and enough teriyaki sauce to coat it in a plastic bag that can be sealed. Refrigerate it for at least an hour or up to 12 hours to let it marinate.
You can either grill or pan-fry the meat. If you choose to grill, make sure the grill is hot enough that you can't keep your hand over the grates for more than five seconds. If you choose to pan-fry, use medium heat and a non-stick skillet.
Take the chicken out of the marinade and put it on the grill. Throw away any leftover marinade.
Cook for 4 to 5 minutes on the first side; flip and immediately add the cheese to each piece.
Cook until the cheese melts and the chicken turns slightly brown and feels firm. Then take it off the heat and keep it aside..
After taking the chicken off the grill, put the pineapple slices and the buns on it. Grill them until the buns are slightly crisp and the pineapple is tender and browned, flipping them once after about 2 minutes.
Place chicken, red onion, jalapeño slices, and pineapple on each bun. You can add more teriyaki sauce to the chicken if you want.