In the great Greek revival, two years ago, one thing went missing – the chorus. In modernising ancient tragedies, from Medea to Oresteia, writers and directors tended to whittle them down into taut human dramas about families in turmoil. Choruses got cut or scaled back. A few remained in full, but to little effect. The National Theatre's Antigone had a smattering of suits, civil servants in stasis, while zombie-like waifs juddered through its Medea.

Here, then, is choral power unleashed. David Greig's clipped version of Aeschylus's Suppliant Women makes them its protagonist. A crowd of young women, drawn from the community, just as Greek dramas recruited locals on tour, stand onstage in a huddle. Colourfully, even cacophonously, dressed, they're refugees, fled from Egypt to escape enforced marriages. Stood outside the Greek city of Argos, baring suppliant branches bound up with white rags, they're seeking asylum; sanctuary from male violence. They sing-speak as one: "The worries of women and exile are endless."

Plot-wise, it's simple: the women pray to new Gods and plead Argos's king to offer them safety, forcing his hand with the threat of mass suicide. Essentially, it's a series of supplications, women hoping for help, but its power resides in the force of its staging. Drilled by Mary King, the chorus beat out their sentences in sync, words set to rhythms backed up by drums. They move as a unit, skipping and stamping and standing their ground; vulnerable and mighty at the same time in Sasha Milavic Davies' choreography. It's a ritual display that bypasses the brain and gets into your body. When they fall silent, it can stop your breath. The physical, vocal presence is such that you cannot but feel for them – or, indeed, feel with them.

Beauty only exacerbates that. On Lizzie Clachan's unforgiving breeze-block floor, the women celebrate beneath clouds of confetti and sit, in the dark, clutching candles in jars. Exposed outside the city, the threat of male violence is a constant. Soldiers come carrying clubs against their spindly branches. Pirates bear torches in the face of their tealights, and they flee like fireflies through the night.

This is the refugee experience abstracted; the same as it was, at heart, two millennia ago. That is made both less familiar and more; less, because it strips out the imagery we've grown so accustomed to, life-jackets and hijabs and rafts packed with people; more, because these women are like us, of us, are us. In another world, another moment, they really could – would – fall foul of the same fate. In stripping out the specifics, detaching itself from this crisis or that, The Suppliant Women states the plain case.

In that, it wrestles with the ethics and politics of asylum. When Oscar Batterham's King Pelasgos, slick-suited as a Macron or an Obama, strides out to meet them, he weighs up his options: shut the women out or invite a foreign war in. Call it Merkel's Dilemma. His heady tenor makes him all thought, and Pelasgos needs to classify – "Are you maybe Ethiopian?" – where all he should do is feel. Towards the end, Greig's script wrangles with assimilation. The city presses the suppliants to marry, freely, as locals do. The women push back and refuse. In the abstract, it's simple: offer sanctuary, allow space, trust that new arrivals will return that respect.

All this is a return to theatre as ritual, and The Suppliant Women follows the old structures of Greek theatre. Its tone is ancient and contemporary at once, with echoes of Beyoncé and Hamilton in its sound, but its form now feels somehow alien. Beginning with a libation – the offering of wine – it reminds us that the Greeks thought theatregoing a civic duty. In its clear-headed reasoning and its full-bodied feeling, The Suppliant Women reminds us just why.

The Suppliant Women runs at the Young Vic until 25 November.