A co-production between Ireland's Druid Theatre Company and New York's Atlantic Theatre, the show is directed by Tony Award winning Irish director Garry Hynes. It presents a pitch-black lampoon of Irish rural life, which it skewers relentlessly for two hours.
"We followed that up with two other plays, 'The Lonesome West' and 'A Skull In Connemara' - and they soon became known as the Leenane trilogy.
"Martin and I had been talking about a new production of 'The Cripple of Inishmaan' in New York for some time and he wanted it done but wanted it done in a particular way. So we decided to make a co-production of it between Druid and Atlantic."
With the help of a unique agreement between American actors equity and Irish actors equity - where both sets of Irish and American actors performed together in Ireland and here in the U.S - Hynes managed to put together the first-ever full co-production between an Irish and an American company.
Hynes originally discovered McDonagh as a fledgling playwright, and she was the first to produce and direct his scripts onstage.
Their relationship has deepened over the past decade as the awards and plaudits rolled in. Has this success changed him?
"I would say essentially it hasn't changed him," says Hynes. "In his twenties he was literally holed up in his bedroom writing these plays for two years and had never even been to the theater much. He had certainly never seen a production of his plays.
"But he then became one of the most outstandingly successful writers in the English language in a very short space of time - and that process changes you to some degree - but his essence is the same. His skill as a dramatist and as a man of the theater was evident from the very beginning."
Playwright McDonagh, 38, is having a great year.
His debut feature film "In Bruges" - which pleased critics, but failed to ignite much public interest when it opened in January - was unexpectedly nominated for three Golden Globe awards. Alongside the best musical or comedy nomination, "In Bruges" picked up two best actor in a musical or comedy nods for its stars, Irish actors Colin Farrell and Brendan Gleeson. McDonagh also received an Academy Award nomination for Best Original Screenplay.
Although McDonagh's doubters often accuse his plays of having a cartoon quality, Hynes is having none of it. "I feel there is a basic reality to his plays and it's fundamentally important to him that it's reflected in them. I think that's what he was looking for in this production that he might not have seen before," she says.
"The Cripple of Inishmaan" begins by referencing a real life event, when a Hollywood film company shot the famous "Man of Aran" documentary on the Aran Islands in the early 30s, capturing the harsh lives of the island dwellers.
In McDonagh's play a young crippled boy named Billy, played with by Aaron Monaghan, sees his chance to get off the island and pursue his dream of becoming a film star.
"The 'Man of Aran' documentary was supposed to be an authentic look at the life of the islanders," says Hynes. "But as we know now that wasn't true. They used a lot of technical tricks to make the ocean waves look bigger than they really were. In the film islanders went out hunting for a shark, but in reality they hadn't done that for decades.
"Martin takes the glamorous idea of the filmmakers coming to the island and he uses that as his jumping-off point. As a playwright he has the Irish insiders perspective from spending long summers in Connemara whilst growing up, and yet he has the outside view of a Cockney Londoner, which is what he is."