Got this one from PDQ Bach...
What is the question to which the answer is "chicken teriyaki"?
What is the name of the world's only living kamikaze pilot?
That one was old when Johnny Carson was a fetus!
It's still funny, though.

Here's another "question my answer" joke:
The answer is Cock Robin. What's the question?
"What's that you're putting in my mouth, Batman?"