Accessible only by stairs and freight elevator, the thirteenth floor of the Algonquin Hotel contains a laundry room, an office used by the housekeeping department, and a few rooms of storage. No bon mots have been recorded there.

“It was so cluttered,” Manuela Rappenecker, the hotel’s General Manager since 2014, said of her first trip to the floor. “I was looking to clean up a little. I’m kind of a minimalist.” Luis Ortiz from housekeeping was there to assist her while she poked around. To the left of the dryers, Rappenecker noticed a pile of carved wooden posts. They looked old. When she asked Ortiz about them, he led her to a room down the hall and pulled away a blanket to reveal the missing piece: a large round table top.

If they had been at the Iroquois Hotel down the block, or pretty much anywhere else, such a find would be of little interest. But they were at the Algonquin, a place tied up with that piece of furniture like no institution since the Court of King Arthur, and the subject of nearly as much myth-making.

I received this tip by chance shortly after Labor Day weekend, in an email from my college roommate, Nicholas Sciammarella. I had run into him outside one of Brooklyn’s many biergartens, where he and a friend were working their way through a pair of Pilsner-filled glass boots. Nick, a hospitality administration major, told me that he had just been named the marketing manager for the Algonquin, then a new addition to Marriott’s “Autograph Collection.” I congratulated him on the appointment and ordered a stein of dunkelweizen.

I have never gone out of my way to visit a writer’s birthplace or gravestone. For me, the infinitely-reproducible text is the thing, not the original manuscript. I’ll take a quality paperback over a first edition any day. And yet, when Nick wrote the following week with news of the table’s discovery—or possibly rediscovery—I found myself asking him if I could see it up close.

I was initiated into the cult of the Round Table as a teenager. The idea that making fun of your friends over lunch every day was, in fact, an art form seemed right to me. In a flash, I went from wiseass to fledgling wit. Years passed, and with them other enthusiasms, but for me, the Round Table never lost its mystique.

The Round Table became a proper noun largely through Franklin P. Adams’s Herald-Tribune column, “The Conning Tower,” which Adams filled with the best of the group’s one-liners, some of which happened to be his own. Every Johnson needs a Boswell, and Adams was a bit of both—not to mention a self-styled Pepys. A lot got written down, more than enough to justify the hype.

Here’s Adams on a Spanish nightclub fire: “Don’t put all your Basques in one exit.” Dorothy Parker’s note to a New Yorker editor: “Too fucking busy, and vice versa.” Robert Benchley’s telegram from Venice: “Streets flooded. Please advise.” (The Round Table’s best-known quip, “Why don’t you get out of those wet clothes and into a dry martini?” is both misquoted—it’s “that wet coat,” not “those wet clothes”—and misattributed. Credit should go to Mae West.)

But the corpus seems fragmentary when measured against a conservative estimate of the hours Adams and his circle are said to have spent around that table. The greater part of the legend may lie in the gaps which get filled in by our imagination.

So: was this round table the Round Table? “I got here 22 years ago,” Ortiz told me. “In 1995 or 1996, they removed the round table and put it in the sub-basement, then they brought it up here. I wrapped it up really good so it wouldn’t get damaged. At one point, they wanted to get rid of it, so I asked for it and they said yes. I was going to take it, but I didn’t have enough space. My boss asked a couple of times, ‘When are you going to take the table?’ But it wasn’t in anybody’s way, so they didn’t push it too much.” For at least eighteen years, while the hotel below was sold, and re-sold, and the surrounding neighborhood of Times Square was rendered unrecognizable, the table sat under that blanket.

In an appraisal commissioned by Ms. Rappenecker, Joseph Ragazzi, of the Ragazzi Gallery in Flushing, determined the following: the table is made of oak; it is “early 20th century”; and “generally it has an English Tudor influence.” (Apparently, there is also some “carved gadrooning at the circumference edge”.) But is it the Round Table? Ragazzi, despite his considerable experience, is not qualified to say. Forensic analysis is no help either since it would have been covered with a tablecloth during the meals in question. And if a scraping did turn up trace amounts of Heywood Broun, prospective diners might lose their appetites.

The next question was: how long had the table been in use? I consulted the Algonquin’s institutional memory, a waiter named Chuck Shah. Shah, who moved to New York from Cyprus in 1978, had worked at the hotel for 33 years, through four major renovations and five owners. “Every regular had his own table and house account,” he told me. “There used to be a telephone booth over there”—he gestured toward the lobby—“and a shoeshine stand over there.” The renovations rolled back before his eyes. “As the years go by,” he sighed, “everything change.” And the round table? Shah remembers seeing it on his first day in 1981. There the trail goes cold. A retired Rose Room waiter might be able to tell you if the table was on the restaurant floor in 1971, or possibly in 1961, but not whether it was there in 1919, the start of the “ten-year lunch,” and the literature is short on physical description beyond the word “round.”

Still, evidence isn’t everything. “Maybe five years ago, a guest came and asked me about the round table, because she didn’t see nothing round down there,” Ortiz said. “I told her it was upstairs. She said, ‘Can I see it?’ I figured, I don’t think I’m going to get in trouble for this, so I brought her upstairs. Then she said, ‘Can I touch it?’ I said, ‘Of course.’ She was very happy about that.”

The round table currently rests beneath a group portrait of “The Vicious Circle” painted by Natalie Ascencios in what is now called the Round Table Restaurant. Its dark wood surface is bare, perhaps because white tablecloths have gone out of fashion, or perhaps to emphasize the table’s purported status as an artifact.

You can reserve it for lunch, just as you can eat with your hands at Medieval Times in Lyndhurst, New Jersey, to make believe you’re living in a lost civilization. Even if this round table were the Round Table, the world of the Round Table is gone. Publishing is no longer clustered in midtown, or referred to as publishing. And hotels do not extend credit to writers, no matter how clever they are.

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Ash Carter, an editor at Esquire, is working on a book about Mike Nichols.