* Combine the chicken and enough teriyaki sauce to cover in a resealable plastic bag and marinate in the refrigerator for at least 30 minutes and up to 12 hours.
* Heat a grill until hot (you shouldn't be able to hold your hand above the grates for more than 5 seconds). Remove the chicken from the marinade and place on the grill; discard any remaining marinade. Cook for 4 to 5 minutes on the first side; flip and immediately add the cheese to each breast. Continue cooking until the cheese is melted and the chicken is lightly charred and firm to the touch. Remove and set aside.
* While the chicken rests, add the pineapple and the buns to the grill. Cook the buns until they're lightly toasted and the pineapple until it's soft and caramelized, about 2 minutes per side. Top each bun with chicken, red onion, jalapeno slices, and pineapple. If you like, drizzle the chicken with a bit more teriyaki sauce.
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