Thanks for your replies,
I guess my edit was missed.
I am even more abashed than if I had had to take the bike to the shop.

It was skipping on the chainring, not the cassette.
I had put on a new chain.
When I put the old chain back on it worked fine.
I have ordered new chainrings.

I must say, this is the first time I have ever had to replace a chainring, and I don't let my chains get too long before replacing them, so I was blindsided by this and the fact that my friend said he saw the chain skip on the cassette.

Oh well, don't believe what you hear, and only half of what you see!