I've heard about this for decades, and since it involves my all-time favourite comedian, it always gets my attention.

Did Groucho Marx actually say what many consider one of the most off-colour jokes on a radio network ever uttered or is it just a myth? 

The answer may never be definitively known, but there's increasing evidence, even all these years later, that he didn't. But somehow it's etched itself into the lore of the medium's otherwise storied history. (Either way, I'm sure much worse things have been said over the air by now.) Maybe people just want to believe it happened. 

You can decide for yourself with the "evidence" presented at the site below. 

Did the Dirtiest Joke in the History of Radio Really Happen?