9 speed chain doesn't fit 9 speed cassette In all my years of working on bikes, this is a first. Bought a new 9 speed KMC chain and 9 speed cassette to replace a worn 9 speed drivetrain recently (single chain ring). Went to put everything on tonight, except the new chain is way too short -- even on the smallest cog the derailleur is so stretched I'm afraid turning the cranks will rip it off the hanger. 

Comparing the new chain to the old chain (also a 9 speed chain, in case it isn't clear) shows that the new chain is about six inches shorter. I don't know how many links are in the old chain, but the new chain supposedly has 116 links and the highest link chain I can find on the internet is 120. I've never had so much difficulty overhauling a 9 speed drivetrain before.

Can anyone explain what the hell is going on here? I've got pictures on my phone I can include if the description doesn't make sense.
Pretty simple - the new chain is too short. Maybe you bought a chain with too few links, maybe it's a production error. 

The pitch (distance between pin centers) of bicycle chain is 1/2", so it's easy to count links by measuring. 

Chain length required is determined by chainstay length and largest chainring and sprocket size. Usually you get a chain a few links too long and cut it to size and re-join. When replacing a chain you can use the old chain to size the new one. If the old chain is lost chain length can be determined by fitting to the bike. Park Tool has a good video on how to do that.