Besides keeping them on ice on the way up, I'd freeze them solid before the trip.
You'd probably get into trouble if they warmed up to 60+ for a more than a day.
Salt them a lot. Didn't the early explorers use lots of salt as a preservative?
...I wonder... might there be some air-tight plastic bags, something like zip-locks, that you could put your bbq chicken into, then put bag and all into boiling water for some number of minutes. You would have home-preserved bbq chicken.
Or you could just go to the grocery store and buy those foil pouches of ready-to-eat chicken.