Actor Mark Rylance, who stars in the Broadway play ‘Jerusalem,’ is seen in the Music Box Theater in New York. (Jennifer S. Altman/FOR THE WASHINGTON POST)

In Broadway’s Music Box Theatre, the chickens get their own dressing room. The Tony-winning star of the show does not.

If the, er, pecking order sounds a bit out of whack, consider who this particular star is, and his irreverent disregard for the more ceremonial aspects of his chosen profession. This is a man who, after all, facing an audience of his peers and several million viewers on Tony telecasts, fashions his acceptance speeches out of blank-verse writings by a poet from Duluth, Minn.,with nary a word of clarifying context.

Yes, we are talking about Mark Rylance, the 51-year-old dramatic virtuoso who in the past three years has given three of the most talked-about straight-play performances on Broadway and has taken home two best-actor Tonys in the process. First, there was his riotous turn as Robert Lambert, the addled Wisconsinite who stumbled into a sexual menagerie in “Boeing-Boeing.” That resulted in Tony No. 1. Next came his astounding commission of comic coarseness as Valere, the outrageously foul mound of Gallic flesh in the Moliere-esque comedy “La Bete.”

Now, Rylance is leaving playgoers’ mouths agape again with his portrayal of a debauched, charismatic squatter in Jez Butterworth’s “Jerusalem,” a three-hour serio-comedy that also features a gallery of fine young actors playing his checked-out acolytes; manifestations of sex, drugs and rock-and-roll; and the aforementioned chickens. The show, embraced by critics, who named it the best foreign play of the year, extended its Broadway run until Aug. 21 after Rylance secured Tony No. 2 for his performance. Then the play returns to its originating city, London, where it takes up residence in October for a 14-week engagement in the West End.

To be crowned a veritable comedy king of Broadway — no doubt “Jerusalem’s” box office is sustained by his rousing, morally gray central performance — is a wildly unexpected career bonus for this classical actor, who in 1989 played a memorable Hamlet for the Royal Shakespeare Company. And between 1995 and 2005 he was the status-quo-challenging artistic director of Shakespeare’s Globe, a re-creation on London’s South Bank of the Elizabethan theater in which many of the Bard’s plays were originally staged.

“I’m a Broadway actor,” he declares, the novelty of the concept alight in his eyes. “And I never even imagined being a Broadway actor.”

Born in Britain but raised in the United States, Rylance seems to exist professionally on the metaphorical outskirts that his Rabelaisian “Jerusalem” character, Johnny “Rooster” Byron, inhabits on the stage. He’s acquired a reputation as a maverick, but his “Jerusalem” director, Ian Rickson, says his talent doesn’t necessarily emanate from an outsider’s instinct.

“Yes, he’s a genius; yes, he’s mercurial,” Rickson says by phone from London. “What’s talked about less is that he works really, really hard. It’s not that he just puckishly picks up things in the wind. Look at his notebooks. Look at his physical regime. Like the best actors, he’s really energized by working.”

In the hour or so before cosmetic preparations begin for his absorption into the character of Rooster Byron — a makeup person will dragoon him for the nightly application of tattoos — Rylance settles into a discussion of his bi-national roots and other aspects of his curious route to stardom in Times Square. To find him in his communal dressing room, the one at the top of the stairs that he shares with half a dozen men in the cast, one goes by the heavily air-conditioned room in which a clutch of chickens passes the time in a spacious pen, awaiting their own cues. (Onstage, the chickens can be seen scrounging for morsels under Johnny’s eyesore of a trailer, parked in the woods, within range of the disapproving residents of English suburbia.)

Rylance’s dressing table, in a cramped corner, continues the poultry motif: A picture of a rooster is taped to his mirror. “I played Hamlet when I was 16, in Milwaukee,” the actor says, as other cast members wander in and out, some looking harried and intense, others exchanging bits of banter with him. His British parents, both English teachers, brought the family to Connecticut and then to Wisconsin, where Rylance as a teenager was taken under the wing of a drama teacher who drummed into him preparation and technique.

If American theater-lovers are seduced into believing that great Shakespearean actors must drink at the banks of the Thames, Rylance’s upbringing provides the counterargument. “I think of it now as a real advantage,” he says of first performing Shakespeare as a schoolboy in the Midwest, “partly because he wasn’t the national poet. He wasn’t connected to patriotism here as he is there.”

“It was very unfashionable, very anti-Method,” he adds. “From the age of 12, I was in a very disciplined program, with three productions a year.”

At 17, Rylance was accepted into London’s Royal Academy of Dramatic Art with some embryonic gifts and, by his own admission, a serious case of adolescent torment. “I was acting to get away from my own mixed-up psychology,” he explains. “Looking for someone to be, really.” In the ensuing search he learned how out of step he was with his peers: “I arrived in England thinking that I was an Englishman with a Midwest accent.” But sounding American did not go over well at the RADA.

“I would find there were all kinds of assumptions,” he adds. “I wanted to be unknown. I adjusted the way I spoke.”

Decades on, a division of the tongue still seems to be a part of him. Accepting his recent Tony Award, for instance, Rylance spoke in an American accent. But during the interview, he sounds British, a close approximation of but not exactly like the raucous Wiltshire character he portrays. It’s not at all clear how conscious any of this is. “My dialect is a mixture of a lot of different things,” he says. “What would happen when I would play an Irishman is, I would sound like an Irishman for a few months after.”

His early experience with the Royal Shakespeare Company was not a happy fit for him, even if, in retrospect, he appreciates the exposure he had to legendary directors such as John Barton and actors such as Michael Gambon. (He says the company leadership perversely forbade Gambon and other older stars from passing on tips to the next acting generation.)

“They were like a very successful football team. It was all a bit of a love-in,” he says of Trevor Nunn and other leaders at the time. Their ethos, he adds, felt oppressive. “The older actors used to joke that it was a kindergarten run by the Mafia. It was a style that they were doing, and it wasn’t being investigated.”

Eventually he set off on what he calls “an alternative path,” founding a traveling company with the woman he’d later marry, Claire van Kampen. That experience led to his signing on as founding artistic director of the Globe, a job that he loved and that brought out the combative side of his nature. “I was at that time probably strident. I fought hard for it.” He resented what he thought was the lack of seriousness with which British drama critics took the enterprise, and he still feels that way. “We were challenging the RSC,” he says, by way of explaining the response.

But the sometimes-hostile response of an audience, he adored. Once, while he was playing Cleopatra — this is Elizabethan theater, remember — a heckler in the open-air space shouted: “What’s wrong with having real actresses? Why do we have to have these [epithet]?” After a moment of shock, he and the other actors playing women recovered — and luckily, Rylance says, his character’s next line was an aptly withering retort that the audience roundly applauded.

Burning out finally (“I think they’d had enough of me after 10 years; I got tired”), Rylance parted ways with the Globe. Soon commenced this extraordinary freelance winning streak, on both sides of the Atlantic. And as a result, that most outlandish of phenomena — a Broadway star not minted in another medium — came into being.

Rylance is happy to continue to reflect, but the routine — and the chickens — of Broadway beckon. “Time for your tattoos,” says the makeup lady, standing in the doorway. Almost time again, too, for the actor to crow.