I was a generative linguist in my previous career and no linguist that I know has ever heard of this Chomsky challenge thing. It’s hard to prove that something doesn’t exist, but I’m fairly sure it doesn’t.
It's conceivable, but I doubt it, for the reasons I mentioned. If Chomsky created this thing then presumably his wife can dig out some kind of record of it (as she apparently handled the communication with Epstein's office). So far we haven't seen it.