Roman's post over in the "program" sub-forum about the 1938 New York City had me Googling about the Burns/Benny/Chapereau smuggling case - and I came across this which should be interesting to all here - and is oddly appropriate considering some of the political happenings these days.
The FBI has a section on their website of files on famous folks, Jack included! No real dirt (what were you expecting!?) but it does offer some interesting insight into the Chapereau smuggling incident. The file is almost entirely about the smuggling case, with a couple of banal latter day requests for clearances to the white house or other government buildings.
This whole thing really went down at a fascinating social and political moment in US History - I doubt if the US wasn't teetering between sides in the war that this would have amounted to anything at all. There is clear evidence of this being some kind of anti-semitic lash at the Burnses and Bennys by the Nazi-sympathizer maid who was a key witness in all of this. One unattributed allegation claims that the Burnses were dope fiends, which is the reason why "Gracie always wears long sleeves"! (Of course, the real reason is her arm was badly scarred as a child).
Gracie Allen's file is also up but it appears to be pretty much a duplicate of the Benny file.
http://foia.fbi.gov/foiaindex/benny.htm
I had some real trouble with these PDF files using internet explorer, it worked much better in firefox for some reason.