Former Senator Paul Simon writes in his autobiography about Club Prevue (the book is available on Google Books). He writes that the club was well known, lit with a neon sign, and not afraid of local law enforcement. After his efforts, the club closed up shop. I can't tell from the excerpt, but it appears Simon may have been involved with a prosecutors office. There are references in his book to other illegal clubs that were closed in the early 1950s as well.

Link to Google Books - Paul Simon autobiography
http://books.google.com/books?id=CPpP98ESkiIC&pg=PA45&lpg=PA45&dq=%22club+prevue%22+illinois&source=bl&ots=MkkFMob5zs&sig=WXOe50fMpMHixcYWgecJXHjyTKE&hl=en&ei=hq1rSvHJH4ioNoWTgPkG&sa=X&oi=book_result&ct=result&resnum=3