Transfer Case chain play?

Oh yes, way too loose. Thanks for the video, it helps, is the chain and sprockets new? If not, this will be the problem. Here is the part number for the correct chain:

32 - Drive Chain - 1L5Z7A029AA $135.00

Let us know what you find.

Chain is not new. Truck has unknown mileage. It was a farm truck. Odometer got stuck at 69,000 miles. I am guessing 300,000 miles or more .
Thanks for the part number! Gears are old too, probably the same mileage.

Yep, this will cause the looseness of the chain, let me know how it goes when you get the new part.

Update. I bought a new chain, and the play was exactly the same. I installed it anyways and put the Xfer case back into the truck. It works perfectly. Unfortunately, it still leaks. I sealed it really good this time and let it sit for 3 days. Then I filled it with oil and let it sit for a few hours and then I installed it. I drove for about 10 minutes and as soon as I drove into my garage, I checked for leaks and sure enough, there was a quarter size drop on the floor within only a few minutes. Ugh. I can't get that case to seal...Now what? Take it out again, I guess.

Circled in red is a bolt that is not supposed to be there. I added it because the oil is leaking through the top inside of that hole (which I apparently did not put enough sealant on). So, I put a bolt in there and silicon around it and tightened it. I used Permatex ultra-light blue, which I think is wrong, it should be Permatex Black or Grey. What do you think?

Is this a stock transfer case for this truck? It does not look like the normal transfer case I see in these trucks for this year?

Borge Warner 1354. I took it apart again and split the case and cleaned it all up and I Found a little tiny burr (only about .020 in.) just above where it was leaking. So, I smoothed it out and used black RTV and put the case halves back together and let the case sit inside for a couple of days now. This should stop the leak...

Yep, that will cause a leak. Let us know if you need anything else.