Grill each pineapple ring on medium heat until grill marks appear on both sides. Set pineapple on the upper grill rack to keep warm or remove from grill when finished.
Season each raw chicken breast with salt and pepper on both sides.
Grill for 3 to 4 minutes on each side until the internal temperature reaches 160 degrees Fahrenheit.
Add 4 slices of ham on top of each breast. Then add 1 slice of cheese, and 2 grilled pineapple rings on top of each chicken breast.
Close lid and let heat until cheese melts; about 2 minutes. Make sure the chicken has reached 165 degrees Fahrenheit, then remove from grill and enjoy!