I replaced my chain. I also replaced the oil pump pickup. I think they both cost me $125. I didn't replace the rear seal, and it started leaking about 2 weeks later. I'd replace that. You can get it online for $13 or at the dealer for $32.
I did NOT remove the transfer case, I just removed enough to get to the chain.
I didn't want to spend the $250+ for new gears, so I broke it down and looked at them. They "seemed" to be fine, so I just replaced the chain.
Everything works great now.
I would have liked to bought a overhaul kit and new gears and gone through the whole thing, but I'll wait and do that when I do the SYE.
So to answer your question. Yes you can do it under the vehicle. Yes you can just replace the chain. Use brake cleaner and really clean everything well. Keep in mind that if you are doing it cheap, you may wind up having to do it again, and again, or you may get luckly like I did.
It just depends on what you find in there.
My original idea was to get a spare transfer case and swap then work on my original, then swap it back. Didn't work out NP242 were going for $350+