Depending on how much use your transfer case has seen, it is possible for the chain to "stretch" some and allow skipping. Changing the fluid wouldn't hurt, and would allow you to see how much, if any, metal is in the fluid. The correct fluid for your transfer case is a dealer only item and is a blue/turquoise color. On some transfer cases, you can also check you chain slack through the fill hole. I just do not remember off the top of my head if that is possible with this transfer case.
The rear seal is not a hard job and could be done in the drive way in an afternoon (probably 2 or 3 hr for the first time). No 'special' tools required. It is also a relatively inexpensive repair. The cost of changing the fluid in your rear differential plus the cost of a seal (~$10-15). The LTZ comes with the limited slip rear differential, but it does not require a friction modifier. I tend to just use a good GL-5 gear oil.
EDIT: if you find chunks or slivers of plastic in the transfer case fluid, that is from the chain guides.