Coward was knighted in 1969
The script for Long Island Sound was only rediscovered three years ago.
The play began life as a short story based on a nightmare evening Coward attended in the US in 1937.
He completed the script 10 years later but decided against producing it largely because it was critical of real-life New York socialites from the day.
The play is now going head to head with a current Broadway revival of Coward's classic Private Lives.
Long Island Sound is unusual for Coward as it features only one Briton and it is his only play to be set in the US.
Mixed reception
Actor Simon Jones stars as a distinguished English writer who has his hopes of a quiet country weekend in a Long Island home dashed by a string of loud-mouthed high society Americans who also come to visit.
The production has split the critics.
The New York Post described it as a "fast, funny comedy about an innocent among sharks".
But Newsday said while it had "glimmers" of Coward drollery they remained "few and very far between", meaning "all those charmless Americans remain, alas, nothing but charmless".
Private Lives stars Alan Rickman, who is up for a prestigious Tony award, Broadway's equivalent of the Oscars, after the show's transfer from London's West End.
Coward was one of the UK's most famous playwrights.
Born in 1899 his first play, a light comedy called I Leave it to You, had a brief run in the West End when he was just 18.
Soon he quickly established himself as a leading wit, writing such classics as Hay Fever, Design for Living and Blithe Spirit.
He was knighted on his 70th birthday in 1969, and he died four years later in his Caribbean home.