Smear a good dollop of cream cheese on each half and apply a chunk of the Monterey Jack cheese.
Place each on a hunk of flattened chicken breast and spiral wrap each with a strip of bacon, secured with toothpicks.
Sprinkle each one with your favorite barbecue rub and put them on the grill. Turn them every 5 minutes or so until the chicken is cooked, probably around 20 to 30 minutes.
Oh, I almost forgot, apply barbecue sauce about 10 minutes before they are done. I do this multiple times to build up a very cool coating of sweet and tangy sauce.
When they are done, remove from the grill, let them rest 5 minutes or so and serve. Be prepared to hear some accolades, because these babies are very, very tasty.
Happy grillin'.