Not so long ago Angel Olsen was a promising singer-songwriter out of Chicago. Times have changed. She’s moved to Asheville, and her music has evolved into something far grander than the singer-songwriter tag suggests. And Saturday, as she made her latest return to the Windy City with an early evening set at Pitchfork Music Festival, it was clear that Olsen has more than lived up to that initial promise.

During Olsen’s tour in support of My Woman, the first thing you see is her band, an assortment of women and men all dressed in matching light blue suits. They walk out, take their places, and begin vamping through the first song, and not until anticipation has reached fever pitch does Olsen come sashaying on stage and grab her guitar, made up like the retro pop and country singers her music often evokes. It was a neat trick last fall at the tiny upstate New York festival Basillica Soundscape, but in front of tens of thousands in a large park west of downtown Chicago, it was a superstar gesture.

Olsen has the goods to back it up: the songs, the swagger, the voice! [Please observe a moment of silence to contemplate the gift that is Angel Olsen’s voice.] Over the course of three increasingly awe-inspiring albums, she’s established herself as one of the most stirring and singular musicians on the planet. On a foundational level, her songs are still just a few guitar chords and some vocal acrobatics, same as when we first encountered her five years ago. The focal point remains her singing, capable of delicate trembling that can ease you into a calm and fierce outbursts that just rip open a song and spill its guts out. Yet she’s increased her music’s dynamism with smart aesthetic choices, dressing her songs up in much the same way she dresses her band — classic sounds tweaked in subtly modern fashion and elevated from coffeeshop intimacy to stadium status.

OK, so Union Park isn’t quite the size of Soldier Field, but with Saturday’s performance Olsen and her band made it clear they’ll be very comfortable opening for Arcade Fire later this year. They began with “High & Wild” from 2014’s Burn Your Fire For No Witness, expanding from a roots-rock ramble to a gnarly climax built around a bluesy power chord riff. From there they launched directly into “Shut Up Kiss Me,” a song that grips you as urgently as its subject matter demands, from its bracing rock ‘n’ roll cadence to Olsen’s howling, bellowing, tour-de-force vocal performance. Two more straight-up rockers followed, with “Acrobat,” the hushed intro from Olsen’s 2012 debut Half Way Home, serving as a bridge to the set’s less visceral but even more compelling second half.

Olsen spent her last three songs stretching out, unfurling three tracks from the back half of My Woman in sequence. There was “Sister,” the eight-minute epic that serves as the album’s centerpiece, building slowly from a low-key Roy Orbison-via-Velvet Underground ballad into the kind of glorious guitar symphony I wish Wilco was still writing. There was “Those Were The Days,” a song that imagines what Bonnie Raitt’s attempt at dream-pop might sound like, extended into a beautiful series of peaks and valleys. And there was “Woman,” another eight-minute swoon that begins as a weepy country ballad before going full Joplin and, ultimately, taking its sweet time descending from the mountaintop. These songs gave the audience a chance to sit back and appreciate what Olsen’s band members bring to the table. It’s one thing to burn through some rock songs with power and fury, and it’s quite another to make such lengthy excursions surge and soar. And watching Olsen and her primary back up singer push their voices skyward in tandem was one of the weekend’s purest delights.

Even the moments between songs were entertaining. Olsen sprinkled deadpan jokes about the confessional nature of her music (“It’s hard to be real with everyone in your life,” she counseled, adopting the expression of a therapist but with a grin sneaking out of the corner of her mouth). She cracked wise about the need to venture outside of the VIP area to get the best food at the festival. She noted that although she hasn’t lived in Chicago for a couple years, “I know some things.” The banter was slightly awkward, albeit charmingly and charismatically so. Whenever the music kicked back in, there was no such uncertainty, just one of the greatest of her generation in full command of her formidable powers.