A thin metal shield on the downtube designed to protect my carbon frame from a jammed chain came off when I jammed my chain; obviously it was doing what it's designed to do. Any thoughts on what kind of glue to use to stick it back on?

I'd consider installing an N-Gear Jump Stop instead; it will keep the chain from falling off to the inside, which I assume is what happened to you. Better to prevent the problem than try to mitigate the damage when it happens. Besides, digging a greasy chain out and putting it back on it is a pain.

An N-Gear, Third Eye or similar chain "watcher" is a very valuable bit of frame protection but they only work on round or nearly round seat tubes. There is a K-edge chain watcher that bolts to the front derailleur mount so it's useful where the others won't fit. Here is a listing of the verious K-edge models: https://www.acecosportgroup.com/shop/...-catchers.html

A thin coat of rubber cement. That shield on the chain stay primarily protects against damage from chain slap, not chain drop.

It sounded odd but the OP said the shield was on the "downtube" so I'm not sure exactly what he had. As noted, a chain watcher is still a good idea.

I have the K-Edge DIRT-3 on two of my bikes.
Expensive, but it is *so* elegantly simple!

Thanks for the advice gizmos to keep the chain on. My seat tube is anything but round so it may be a challange. Fortunately dropping a chain has been a rare occurance for me.

Also, I mispoke; the one that fell off was on the chain stay. But there is also one on the down tube. It's a Trek Madone 4 frame.