This sounds similar to what happens when you get "chain suck" usually from a muddy chain. However, I suspect it is from a worn out chainring which can behave the same way under load.
Originally posted by Cambronne
This was never much of a problem in the old friction shifter days... Once the chain began to drag the ground, it was time to replace it, no harm done. Now, though, it takes very little elongation to ruin a drivetrain.
Positive NOTE: Chainrings don't suffer much from chain stretch. They'll work fine, even worn down to little pointy hooks... until teeth begin to break off!
I have to disagree with you on this one Cambronne, I have seen many chainrings ruined from stretched chains. Put on a new chain and the thing skips like mad. Replace the chainring and all is better. Also, I still ride friction shifters on my geared bike which this has happened on. This is the thing which taught me to replace my chain frequently. I still have a friend who doesn't follow this advice and as soon as he replaces the chain, all kinds of skipping occur on the middle ring. Seems like he'll never learn.