Chris Rock has locked in a Broadway run in “The Motherfucker With the Hat,” a play by Stephen Adly Guirgis set to premiere at the Schoenfeld Theater in April.Anna D. Shapiro (“August: Osage County”) directs a cast that includes Bobby Cannavale, Annabella Sciorra, Yul Vazquez and Elizabeth Rodriguez. Scott Rudin, the Public Theater, Labyrinth Theater Company and Stuart Thompson produce. Play was originally announced as part of the Public Theater season and had been assumed to be headed for one of the Public’s Off Broadway stages. “Hat” will mark Rock’s Broadway debut. He had been discussed as a casting possibility for “A Behanding in Spokane,” the Martin McDonagh play that appeared on the Rialto last season, but that project ended up moving ahead with Anthony Mackie in a cast that included Christopher Walken, Sam Rockwell and Zoe Kazan. “Hat” joins a slate of Rudin-produced, star-driven play productions that includes a spring staging of “The House of Blue Leaves,” toplined by Ben Stiller and Edie Falco, and a fall revival of “Sweet Bird of Youth” starring Nicole Kidman. Rudin also produces spring offering “The Book of Mormon,” the tuner by the creators of “South Park.” The Off Broadway, nonprofit Public Theater has recently become a regular presence on the Main Stem, with this season’s offerings “The Merchant of Venice” and “Bloody Bloody Andrew Jackson” following in the footsteps of the company’s 2009 Broadway transfer of “Hair.” Guirgis (“Our Lady of 121st Street,” “The Little Flower of East Orange”) is co-a.d. of Labyrinth, the troupe co-founded by Philip Seymour Hoffman. Labyrinth and the Public were previously aligned in a partnership that saw Lab stagings hosted at Public venues, but that arrangement was deemed too pricey earlier this year. Vazquez and the costume designer of “Hat,” Mimi O’Donnell, also are co-artistic directors of Labyrinth. Design team of the production includes Todd Rosenthal (sets) and Donald Holder (lights). “A Life in the Theater,” the David Mamet revival that ends its limited run Jan. 2, is now at the Schoenfeld. “Hat” begins previews March 22 ahead of an April 11 opening. Show is set to run 14 weeks.