Last August, Mr. Wright sat at the desk in his home office in West Austin. On a computer monitor was a document opened to draft No. 78 of “Cleo.” He was preparing for the play’s September debut. Then Hurricane Harvey hit Houston in late August and damaged the Alley, prompting the delay.
In those seven months, Mr. Wright wrote nine more drafts, all while serving as an executive producer for the new Hulu series based on “The Looming Tower” and completing a new book on Texas politics. “Cleo” is now a drastically different play than it was when Mr. Wright conceived it, yet the theme remains the same.
“It’s in some ways a disquisition on love, and how dangerous it is, and yet how essential,” Mr. Wright said. “We’re condemned to have this riotous, unsettling element in our natures and we don’t understand it.”
Initially, Mr. Wright had focused on the affair between Joseph Mankiewicz, the movie’s director and co-writer, and Rosemary Matthews, the script supervisor. He was intrigued with the intertwined destructive relationships at play on the set: from Antony and Cleopatra, whose relationship shook empires; to Burton and Taylor, whose relationship ripped apart their marriages and ignited the gossip pages; to that more prosaic boss-subordinate romance.
Change came when Mr. Balaban got involved about seven years ago. He had met Taylor a few times through the actress Maureen Stapleton, and persuaded Mr. Wright to redirect the emphasis to her and Burton, the obvious stars of the show.
The script still does feature Mankiewicz, an Oscar-winning filmmaker who became overwhelmed with the enormity of the movie, a budget-buster that threatened to bankrupt Fox. Also in supporting roles: Eddie Fisher, the singer and actor who was Taylor’s husband — her fourth — at the time, and Rex Harrison, the actor playing Caesar, whose ego took a toll as his role diminished in the growing shadow of Burton’s Mark Antony.
The actors Lisa Birnbaum and Richard Short portray Taylor and Burton. They were cast, Mr. Balaban said, for their ability to embody both tragedy and comedy, and because they resembled their characters without ever appearing to do impressions of them.
The play starts with Burton arriving drunk to the set, in Rome, to replace the actor Stephen Boyd, who was no longer available after production delays. The idea of using Burton came from Fisher, who unwittingly invited a snake into his own den, according to Mr. Wright.
Burton and Taylor couldn’t keep their cravings secret and the nascent paparazzi captured every blatant minute of their sunbathing and petting.
“There was outrage,” Mr. Wright said. “Nobody had ever seen this kind of thing happening in public before. The tabloids were full of ‘homewrecker.’ ”
The pope condemned the couple, and a congresswoman from Georgia proposed prohibiting Taylor, a naturalized U.S. citizen, from returning after filming. Fidelity was a tightly held American value, yet the pair persisted in flagrant defiance and, in Mr. Wright’s estimation, helped to spark the sexual revolution.
“The Richard Burton Diaries,” published in 2012, was crucial to understanding not only the dynamic between Burton and Taylor but also Burton’s light and dark sides. Mr. Wright’s research also included interviewing sources close to the movie.
“The play ends with a rather brutal scene — a big, knock-down, drag-out fight that you would think would tear Taylor and Burton apart but is actually what ends up cementing their relationship,” Mr. Balaban said. “We wanted to present something that was probably like what really happened with them.”
A 2016 reading of “Cleo” that was part of the Alley’s festival of new works inspired Gregory Boyd, the former artistic director, to stage a production. Mr. Wright is not, however, new to theater. In his career, he has written four plays that have been produced (“Camp David,” “Fallaci,” “Sonny’s Last Shot” and “Crackerjack”) and performed in two of his own one-man shows, “The Human Scale” and “My Trip to Al-Qaeda.”
“I’ve written movies, but typically with a movie, as soon as the director comes on, the last thing he wants is the writer around,” Mr. Wright said. “So you get kind of pushed out. In the theater, the playwright is the final authority, and I don’t mind that.”
On April 17, he will publish “God Save Texas: A Journey Into the Soul of the Lone Star State,” based on reporting he did for an article in The New Yorker. David Remnick, the magazine’s editor, asked Mr. Wright to explain his home state; the writer playfully reminded the editor that he gets paid by the word.
Mr. Remnick was willing to take the risk.
“The secret to Larry is that he writes only about what completely grabs his attention and imagination,” Mr. Remnick said. “Nothing obligatory, nothing on order. He does what he’s going to do. And the results are invariably amazing.”