Of course they did, and it’s available for anyone to look at, heavily redacted of course. The Xerox machines at the FBI a few decades ago were super shitty (a feature not a bug?) so a lot of the pages you can’t make out a damn thing, but other sections are perfectly legible.
If you know anything about J. Edgar Hoover and the FBI, the contents here aren’t too surprising—they were mainly worried that Groucho might be a Commie (if not a Marxist) in the early to mid-1950s. There are countless (redacted) reports to the effect that Groucho had a lot of pro-Communist sympathies but was almost certainly not an actual party member. (I guess the G-men already knew that he’d refuse to join any club that would have him as a member?) There are some interesting references to a quotation of Groucho’s that appeared in the Daily Worker in 1934 that went “The battle of the Communists for the lives of these boys is one that will be taught in Soviet America as the most inspiring and courageous battle ever fought.”
Keep in mind that in 1934 Hitler was running Germany but not yet regarded as an obvious scourge to be eliminated. Still his anti-Jewish sentiments were clear enough. As a well-informed Jewish American it would be weird if Groucho hadn’t gotten interested in Communism around then. Plus for similar reasons the mid-1930s was a high-water mark for leftist and/or pro-Soviet feeling, especially once the Spanish Civil War got going in 1936. A lot of people who weren’t all that political got into trouble later for things they did (and thought) before WWII.
There’s also some business about Groucho and Chico being found guilty in a copyright infringement case in 1937 and having to pay a $1,000 fine.
For some reason Groucho (né Julius) is invariably referred to as “GRAUCHO MARX.” Once we reach the 1960s he is referred to as “Groucho.” I don’t know what’s up with that. In the summary sections of the file there is some background about how musically talented Groucho and his brothers are—the musical talents of Harpo and Chico are well known, but the file also, intriguingly, says this: “GRAUCHO MARX is rated as one of the best guitar players in the country.”
There’s some business I don’t understand from 1957 about someone trying to “extort” Groucho. I can’t tell if it’s just a weird piece of fan mail that was referred to the FBI that they were obliged to look into or something more serious. On that page there is this chilling passage:
The death threat letter sent to GROUCHO MARX from ELVIS PRESLEY fanatics from Brooklyn stating that GROUCHO wouldn’t live through the holidays, might seem ridiculous if it weren’t such a serious offense to send such a threat through the mails.
Again, I don’t know why this is coming up in a section marked “Extortion.”
Finally, there are a few amusing cases where a stray subversive comment from You Bet Your Life somehow ends up in the file, without anyone taking it very seriously. For instance, in early 1960 one of the guests on the show is identified as a “bootlegger,” and Groucho asks him if he is a “bootlegger for the FBI” The page states that “if the question was phrased as [the informant] stated, it was in poor taste but I do not feel that any further action is warranted.”
Similar cases arise when Groucho refers to our country as the “United Snakes of America” and also makes a snide comment about America being full of “arrogant” motorists. I’m guessing that since probably 40% of adult Americans watched those telecasts, a regular uptight viewer no doubt reported Groucho to the Feds and so into the file it went.
You can see all of the pages below, and much more, at the FBI’s own website.