Quick: what rhymes with lysergic acid diethylamide?

In a trippy turn of events, Lincoln Center Theater said Tuesday it would bring to Broadway a new musical exploring the use of LSD in the 1950s by three celebrated individuals.

The musical, “Flying Over Sunset,” imagines encounters with the drug by Aldous Huxley, the English intellectual who wrote “Brave New World,” Clare Boothe Luce, the American playwright who became a congresswoman and an ambassador, and the actor Cary Grant. In the show’s first act, they try LSD separately — which really happened — while in the second act, they use it together — which did not.

The production has an accomplished creative team: James Lapine, who wrote the book and will direct, shared a Pulitzer Prize for “Sunday in the Park with George” and has won three Tony Awards; Tom Kitt, who wrote the music, won a Pulitzer and two Tonys for “Next to Normal”; and Michael Korie, who wrote the lyrics, was nominated for a Tony for “Grey Gardens.”

And the show will be choreographed by Michelle Dorrance, among the nation’s most heralded contemporary tap dance artists, working in theater for the first time. (The libretto depicts Grant as having been an early career tap dancer; in real life, he had performed with a group of acrobats.)