"This is very cool," Adam Driver says as the serene face of the Statue of Liberty comes into view. We levitate around it for a little while, observing the trails of tourists that scurry, antlike, under Lady Liberty’s skirt. The air is smooth and clear—just as our helicopter pilot promised. Then: "Shiiiit!" Driver says, as the machine shudders and dips, then jokingly throws out his arms as though bracing himself against potential disaster. The gust lasts approximately two seconds. The pilot glances back quizzically at this strange tall man with the slightly familiar face. Driver pushes back his longish hair—the indie-rock styling of which may not be so much his as that of the character he plays on HBO’s Girls—and nods. "I’m glad they gave us these fanny packs," he deadpans, patting the life preserver on his waist.

There’s not much Adam Driver is afraid of, certainly not a touristy helicopter trip. "We rode in helicopters in the Marines," he told me on the tarmac. "Also, we’ve been using them a lot in this movie I’m in." He sounded a little embarrassed, like being in a movie is so much less cool than being a Marine. But it was, after all, his second choice of career.

These days it’s rare to encounter an emerging Hollywood talent who is also a veteran—of a Who Wore It Best battle, maybe, but not the actual military. But before Driver became the breakout star of a show about entitled slackers in Brooklyn, he served in the armed forces. More specifically, he was "a fucking Marine who went to Juilliard," as one director put it, in that tone of curiosity and awe Driver tends to inspire.

The helicopter arcs over the Brooklyn Bridge. "There’s my apartment," Driver says, pointing. He sounds a bit wistful, probably because lately he hasn’t seen the inside of it much. Over the past couple of years, Driver has been in the midst of a transformation, from the most unexpected star of a cult TV show to being "probably one of the most sought-after actors around," says director Shawn Levy, who moved heaven and earth—in the form of the schedules of Jason Bateman and Tina Fey—to cast Driver in the role of the perpetually adolescent younger brother in this month’s This Is Where I Leave You. The movie is the first in a veritable avalanche of prominent films Driver will soon appear in, among them Jeff Nichols’s Midnight Special, Noah Baumbach’s While We’re Young, and Martin Scorsese’s Silence. Like a cool band, he’s been plucked from hipster Brooklyn and is in the process of being fully mainstreamed, though he still retains his cred: Last night, he was up late shooting scenes for the fourth season of Girls, even though today he’s leaving for the London set of the latest installment in that blockbuster of blockbusters, Star Wars. I’m looking at him craning his neck toward the chopper window, this quiet, slightly goofy guy whose Adam’s apple, in profile, sticks out roughly as much as his nose, and Driver doesn’t seem like the world’s most likely movie star. But "this kid," Levy says, with mark-my-words import, "is going to be one of the most formidable actors of his generation."

"That’s nice of Shawn," Driver says when I tell him what Levy said. "He’s, like, the kind of person who believes things will turn out good. Unlike me, who believes things are going to go to shit at any minute."