I have a feeling this will sound like a very noob question, but I am not overly mechanically inclined with bikes so I am asking anyway.

I have a 92 Trek 830, which works fairly well still. However, my chain does not like to stay on the 7th (last) gear of the rear cassette. Often when shifting to that gear, it skips right over it and lodges between the cassette and the frame. When it does engage, maybe 1 in 3 tries, it sometimes skips off while going.

The gear itself does not look bent or worn to me. Although I am just eyeballing it.

Is this a sign of a loose or stretched chain? I did have the bike in the shop, but the shop repair guy wrote it off to the geometry of the chain from the front. Maybe it is not optimum here, but it never did jump off at this frequency.

Ideas?

Check your derailleur hanger to see if it is bent, then go to ParkTool.com and follow the procedure to adjust the limit screws (especially the low limit) on a rear derailleur.

Also, I know you posted here because you have a mountain bike, but the Bicycle Mechanics forum is the best place for this type of question. There is lots of good advice available there.

If by "7th gear", you mean the smallest cassette cog, then we'd be talking about the high-limit screw. It's much more helpful to speak in terms of largest versus smallest rather than the numbers on the shifters, since we can't see your shifters.

Yep, smallest cog.

Thanks for the tips and advice guys! Sorry about not finding the optimal forum for the question too!

Everything everyone else wrote x2...
but what that tech said to you? wow, find another tech...
did he/she even check the derailer alignment?, adjust the screw(s)?, adjust the barrel, measure the chain? or the spring tension in the older derailer....?

Both of the recommendations above are possible causes. If the hangar is straight then the limit screw changed or was never dialed in correctly. If the hangar is bent, the limit screw didn't change. IMHO if the hangar appears to be straight, I'd adjust the limit screw and see if that solves the problem especially if all other gear shifting is not having a problem. It's easy to return the limit screw to where it was if it's not the problem. Adjusting a hangar takes a little know-how.
P.S. Also, find a new bike shop. Any shop that dismisses a problem like that without a thorough examination would not gain my business.

My 1990 Trek 820 has a similar problem with the 6th gear. It is time for a new chain and cassette. As soon as I have the money...

Derailleurs are very simple to understand and adjust. If you look at the derailleur from behind the rear wheel you'll notice there are two adjustment screws on it. One screw limits how far the derailleur will swing to the right. The other screw limits how far the derailleur will swing to the left. Your goal is to align the left and right swing of the derailleur to the exact width of the cassette.