The failure of the transfer case on an E53 is a pattern failure. It's not a matter of if, but when you will experience this failure. For some people, the chain inside the case will stretch to the point of causing the cogs to skip a tooth. For others, like us, the splines on the gear that drives the front driveshaft will fail and get chewed up, which means you'll either have to rebuild the case or buy a new one.
In this video I present an overview on what was necessary to remove the transfer case from the vehicle and I then take it back to my shop to dissect it and determine what the exact failure was. I then take you through the process of replacing the chain, if that is your failure, and finally I get it back in the car.