I've puzzled on this since I bought this '91 Schwinn Paramount frame several weeks ago. I thought I'd figure it out on my own, but so far have not.

This is on inside of the right back stay. About 4" up from the drop out. Nothing similar on the other stays.

Chain hanger for wheel changes.

That is a chain hanger, when you are removing the rear wheel the chain is placed on it to allow the cogs to slip out easier and not have the chain on the stay where it can mark up the finish.

Bill

Edit: jiangshi beat me to it, win some lose most

Thanks..... I'd never have come up with that on my own.

Does it eliminate the cussing I've been doing when I'm hot and sweaty trying to get the wheel off to change a tube?

For some reason, chain hangers on steel bikes seemed to have generally disappeared after the mid 80's......
Kinda cheap move by bike makers..... It was a much better/simpler approach to chain management than Campagnolo's Portacatena

The Portacatena was marketed more to serious racers; they could shift onto the Portacatena while still riding and be immediately ready for a wheel change when the support vehicle pulled up. But it came on the market around the same time six and seven cog clusters were replacing five cog clusters. The portacatena occupied space that an additional cog would need, and ultimately The Market decided that more cogs were more useful than the portacatena.

But that doesn't explain why chain hangers on the seat stay pretty much disappeared after the mid 80s.

About half my bikes have a chain hanger. I nere use it. I did a few times, deciced it was more trouble than not usinvg it. YMMV

Probably not, the cussing, sweating and grime are in the constitution, I believe. Its a federal capital crime not to go "Full Monty" when doing the wheel thing. Or maybe its in the Bill of Rights.......

On my Trek it's a little tab built into the drop out

Always used mine every time I take the rear wheel off, on a service stand, or when just transporting the bike in the back of my car. keeps the chain from getting all over the place messing up things next to it or messing up the chainstay and the rest of the frame....
The rear wheel comes on and off much easier too.
Can't figure put why one will not use it if it's on their bike....

A fair question. When I pull the rear wheel off I shift to the smallest sprocket, loosen the skewer, pop the wheel forward in the DOs, then while lifting the bike pull the RD back by the parallelogram until the FW clears the guide pulley. The allows the wheel to fall free. Putting the wheel back in is pretty much the reverse.

Hooking the chain on the hanger requires that I get a hand greasy (I've tried moving it with a tire iron but I must be clumsy, and then the chain has more tension and less clearance.

The only real problem I usually have is the chain falling off the chain rings when I lay the bike down. I sometimes end up with a greasy hand anyway, but I'm I'm smart I don't.

Maybe I need to rethink my technique. But hey, I've had lots of practice!

You do have to get used to slightly tilting the wheel to the left as you pull it back and out of the frame, for the drive side end of the axle and quick release nut to clear the derailleur while pulling back on the derailleur. I'm so used to doing this that it just happens in one motion for me.....many years of practice too, I guess. That's really the only thing that can slow you down taking the wheel off, using the chain peg.
I find them so essential that I've installed on all my CF C&V bikes have, a clipped on version of the peg which is more like a hook. Does not work quite,as well as the brazed on peg on my steel bikes, as the hook tends to turn on the stay from the chain's tension, but still a better situation than having my chain's dangling and banging around when the rear wheel is off, and keeps the chain on the front rings, so there's no messing around up front needed to be done.

I've tried using them a few times, but have always found them more annoying than anything.

To remove the wheel I simply shift to the smallest cog, loosen the QR, loosen the brakes, then give the top of the wheel a good smack and the wheel usually falls out of the dropouts. If the derailleur gets in the way I grab it by the cage (as to not get dirty) and hold it out of the way while I jimmy the wheel out. I do the same when putting it back in.