The trio saw debut album The Bones Of What You Believe crash into the Top 10, and they'll play two sold-out O2 ABC gigs this Thursday and Friday.
Synth-pop tunes like Recover and Gun may be surefire indie floor-fillers, but the band's Iain Cook knows there's a darker hue present as well.
"I think that darkness is inescapable for us, as people, unless we were to write songs in a very calculated way," he explains.
"There will always be a melancholy thread to what we're doing that's at odds with the musical temperature of the songs.
"I don't know whether that's a Glasgow thing, or just us, but I feel it adds depth to it, rather than them being sugar-coated love songs."
All three of the band - Iain, singer Lauren Mayberry and synths man Martin Doherty - are known throughout the local Glasgow music scene, with Iain having played in cult heroes Aerogramme and the Unwinding Hours, Lauren fronting Blue Sky Archives and Martin a member of the Twilight Sad.
It's unsurprising that their crunchy electro-pop comes coated with a more cynical edge, with Iain pondering if their surroundings played a part in it.
"I can't think of many musicians from Glasgow who write facile, summery music," he says. "It's not a dark city, but it does rain a lot, and there's that historical nature of it being a 'hard' city.
"When you've lived here for a long time it becomes hard to separate yourself from the city, it's almost like it's a part of you."
The band has shone brightly ever since last year's Lies single created a stir throughout the internet and beyond when it was released.
While Iain's previous projects have tended towards morose rock, he's been eager to try a project like Chvrches for some time.
"In 2007 Martin was playing keyboards with Aerogramme, we were in America and things were going horrifically," he recalls.
"There was a moment where we decided we wanted to do something on our own that was more immediate and that people could dance to.
"It took about four years to align our schedules and sit down to do it, and there was a definite spark that I'd never felt with any other collaborators."
It was after adding Lauren that things really clicked into gear for the three-piece, with the group quickly realising her voice was perfect to front the band.
Since then it's been a whirlwind of activity, from playing their first gig at the Art School last year ("We were so nervous we were drinking tequila beforehand", recalls Iain) to supporting Depeche Mode in arenas earlier this year.
There's been appearances on American comedian Jimmy Fallon's chat show, a slot on Later With Jools Holland and a flurry of festivals, too, before The Bones of What You Believe was finally released.
"Relief is a really good word to use," says Iain, describing his emotions over the album.
"We've been nervous about it for a long time, as we finished it in June, and there was a lot of nerves about how it would be received."
Yet the group are already getting the itch to return to the studio and start throwing ideas around.
"There's a feeling we're ready to write again, but there's no concrete ideas yet," he says.
"Then again, there never are, we just tend to all go into the studio and see what comes out.
"With other bands in the past there's been a principal songwriter, but that's not the case here - it's all about spontaneity."
The band's rise has come with a more unpleasant side, however.
SINGER Lauren recently spoke out about the growing amount of lewd sexual messages she'd been sent through Facebook and Twitter, prompting plenty of social media reaction.
"For people being irritated by what Lauren said, we don't give a damn about them, we don't want people like that following the band anyway," says Iain.
"What's been great is you see regular girls rallying around it, saying 'I'm so glad you said that, I've got to put up with messages like that too.'
"It was a brave thing to do. We're at a point in our career where we could annoy a lot of people by saying the wrong thing, but this was absolutely the right thing to do."
A lighter note was the band creating a stir by releasing a jokey cover of the Game of Thrones theme on the internet earlier this year. Never mind pop stardom, Iain admits he quite fancies a trip to Westeros
"Game of Thrones have had Gary Lightbody, from Snow Patrol, cameo before, so being in it would be great," he chuckles.
"It'd be okay if we got killed off quickly too, I'd rather be murdered brutally onscreen than just a cameo riding on a horse."
l Chvrches, O2 ABC, Thursday and Friday, sold out, 7pm