The Algonquin Round Table, that famed assembly of literary wits, was born out of a celebration of drama, or at least dramatic criticism. In early 1919, an assortment of writers and critics gathered at New York’s Algonquin Hotel for a lunchtime salute to the work of New York Times drama critic Alexander Woollcott. The team so enjoyed one another’s company that they decided to meet again for lunch the next day.

The rendezvous quickly became a daily event, and it continued for more than a decade; by the end of the Round Table’s reign, tourists would stop by the Algonquin’s Oak Room at noon to watch the writers trade quips. Though best known today as the heart of New York’s literary scene in the 1920s – the fertile soil from which grew the New Yorker magazine – in its own day it was known primarily for its connections to the stage.

Four of the group’s nine founding members were playwrights, including George S. Kaufman and Robert Sherwood; another three were drama critics. Theatrical notables from Tallulah Bankhead to Noel Coward made a point of stopping by to be seen. Twice the group presented short theatrical reviews for the public, the critics among them offering space in their newspapers for leading actors to take a turn at reviewing their efforts.

“The Talk of the Town,” now playing Mondays in the Algonquin Hotel’s famous Oak Room – the very room where the original “vicious circle” first met – probably won’t make the hotel the center of New York theater again. But it celebrates that bygone era with sprightly, endearing, and unsentimental charm.

The Peccadillo Theater Company’s production first premiered at Bank Street Theatre last fall; a regional tour followed. In preparing their script for the Oak Room’s tiny cabaret stage, co-composers and librettists Ginny Redington and Tom Dawes had to eliminate two characters, including the founder of the New Yorker, Harold Ross. But they gained in their place a new personage, perhaps the star of the show: the Algonquin itself.

The hotel has carefully retained the structure and decor of its 1920s heyday, and it graciously lends this ambience to the performers in its midst. The table at which the fauxround-tablers (as group members were known) sit on their small raised platform is the same as those that surround the stage. The somber wooden walls and elegant table settings lend the piece an authority that no black-box production could match.

Ms. Redington and Mr. Dawes’s script lives up to its impressive surroundings. A good portion of the piece is taken verbatim from famous quips left behind by the original circle. Some have been reused enough to pass into the public domain of witticisms (“She covered the gamut of emotions from A to B”) while others still seem fresh (“I never could suffer fools.” “Funny. Your mother could.”). Half the fun of “The Talk of the Town” consists of hearing these one-liners spoken aloud during a routine lunch.

But the authors’ original contributions don’t pale in comparison to the source material. Over the course of nearly 20 years, Ms. Redington and Mr. Dawes have come up with some of the most famous advertising jingles of all time (remember “Plop, plop, fizz, fizz”?) and their venture into musical theater shows a facility with language the round-tablers themselves would have admired. Though the jaunty tunes sometimes seem interchangeable, their skill at wordplay is impressive. They even make the names of the Round Table’s founders all rhyme.

With such airy material at its core, it would have been easy for the play to avoid any degree of seriousness. But for all their humorous proclamations, the members of the Algonquin Round Table shared a fundamental sense of sadness. Almost to a man, the male members of the clique had seen combat in World War I; Dorothy Parker battled with depression and suicidal tendencies. The play tackles these issues head-on, portraying the club’s incessant lightheartedness as a cover for darker emotions.

The expert cast move far beyond simple caricatures in their historical impersonations. Kristin Maloney as Parker is especially compelling, bringing subtlety and vulnerability to her character’s famously caustic persona. Jeffrey Biering commands our attention with his thoughtful portrayal of the arrogant and obsessive-compulsive Kaufman. Director Dan Wackerman rightly keeps his own impact to a minimum, unobtrusively navigating the cast through their small playing space with ease.

None of the members of the Round Table would be so famous individually if they hadn’t been famous collectively. Dorothy Parker’s poetry, Edna Ferber’s novels, Marc Connelly’s plays – none passed into the top tier of the American literary canon. They hold a mythical place in American memory due to their 10-year sojourn at the Algonquin Hotel. We ought to thank Ms. Redington and Mr. Dawes for this return engagement.

Until August 22 (59 W. 44th Street, between Fifth and Sixth Avenues, 212-840-6800).