Q From Janet Hughes: I heard kidding on the square for the first time about twenty years ago from an older gentleman whose origin was the US mid-west. Maybe he was pulling my leg. Where did it originate?
A Somebody kidding on the square makes a joke but means it, too. This is a recent example from an author who uses it a lot:
Priepke was smoking a pipe apparently charged with stinkweed. “Everything under control?” he asked. “Everything except that.” Walther pointed at the pipe. “I thought they outlawed poison gas a long time ago.” ... He’d been kidding on the square; the pipe really was vile.
In the Presence of Mine Enemies, by Harry Turtledove, 2003
It’s a native US idiom, hardly known outside the country. It’s often attributed to the comedian, political commentator and senator Al Franken because of this:
I think he was “kidding on the square,” a phrase I hope will catch on. It means kidding, but also really meaning it. People do it all the time. “Kidding on the square.” If this book does two things, I want it to get “kidding on the square” into the lexicon, and I want it to get Bush out of the White House.
Lies and the Lying Liars Who Tell Them, by Al Franken, 2003.
Readers unfamiliar with it naturally thought it was new and that Al Franken had invented it. It wasn’t and he hadn’t. The idiom is known from the early twentieth century — it turns up in February 1907 in McClure’s Magazine and is often recorded in the years that follow. It's not possible to work out what part of the US it comes from.
Kidding was by then a long-established term of somewhat obscure origin. It was originally low slang of the criminal classes for getting something of value by false pretences; it may be from the slang sense of kid for a child, suggesting that to fool the person was as easy as stealing candy from a baby or that the kiddee was as naive as a child. To kid is to joke, but in particular to fool a person into believing something or deceive them in a playful way.
If you are on the square, you’re honest or sincere, an idea that turns up in other idioms, such as square deal. It may be from a square being an uncompromisingly straightforward shape, but a link with Freemasonry has been plausibly suggested. For masons, a square was a key instrument for accurately measuring a 90° angle, those of the corners of a square (also called right angles because they were the correct or true ones), so that a structure on the square had been properly built. Similarly, anything off square had something wrong with it.
Putting them together produces the idiom that Al Franken used.