alright, fellow gear-heads, looking for input.

I've been going over my 17-bike police "fleet", and getting them ready for Spring. On one of these, I found the chain out of spec, so I replaced it. The cogs and chainrings looked good. Bought one of the SRAM powerlink jobs.

Officer complains of chain skipping.

I take it out, and sure enough, if you're in the little ring and starting out or attempting to climb a hill, it skips. The pedal will go straight down.
I'm convinced it's worn chainrings. So I pull the crank and take it and the rear wheel in to the shop we deal with. One of the mechanics says the crank looks OK, but the cogs are shot. So, 30 bucks for a cogset and I put it back together. Still skips.
Back to the shop with the crank again. They want to sell me a whole new crankset, of course, and I'm thinking chainrings. They say no one is selling chainrings anymore. (This is a Shimano Nexave crank with 5-bolt pattern, thoroughly rebuildable)
Still, the chainrings don't look that bad. How about the freehub? Hmmm, possible.
Back to the station, and I throw another wheel on the rear end, one I know to be OK. Skips even worse.
So, it's not the cogs, it's not the freehub.
I figure either the middle and granny rings are exessively worn, or else it's some problem with the SRAM chain. (standard 8-speed chain)

My next test is to pull an OK crank off another bike and try that.

By the way, these are all quality parts, XT hub and so forth. Shifting, DR adjustment, all spot on.

https://www.sheldonbrown.com/chains.html

Scroll down the the "Chain and Sprocket Wear" section, it gives a pretty good description of what you seem to be experiencing. I've experienced this myself, and only got relief from it after a new chain, cassette, and crank.

Slowly turn the crank backward and observe the chain as it goes through the jockey pulleys on the rder. IF you have a stiff link(s), you'll see the pulley(s) jump.

I don't think this would cause the problem but it might contribute to it: what kind of shape are the jockey pulleys in?

Also, not to say you didn't, but just to suggest: did you check for stiff links?

Another troubleshooting suggestion: switch the chain over to another bike, just to evaluate it separately.

Good luck.

I fooled with it this morning, and decided it's the crank. First, I marked the chain with whiteout at several spots, to see if it, the freehub, or the crank was going to move. Then I locked the rear brake and stood on the pedal.
Slippage, and the chain didn't move.

I yanked an LX crank off one of the other bikes and swapped them, and the bike rode perfectly. Even hard enough pedaling to raise the front wheel up a hill didn't induce slipping.

Fortunately, Nashbar has this very crankset on sale for a mere 36 bucks!

I'd already checked the state of the rear DR, pulleys, and all that as part of my Spring cleanup routine. The guys have a tendency to either under or over-lube chains, and the DRs can get really nasty.