The track is the first to be released from their upcoming album In Our Heads.
In Our Heads is the follow-up to 2010's One Life Stand, and will be brought out on June 11.
The eight-minute video features a continuously spinning camera while the band perform the track in their studio.
Of the album, Hot Chip's Joe Goddard told NME: "It basically sounds like Hot Chip. We haven't done anything particularly weird.
"We've made it on [Kraftwerk producer] Conny Plank's mixing desk that he built. It's a beautiful thing. That's what brought everything together for the new record. It's a continuation with our love affair of different kinds of dance music."
Hot Chip are among the bands performing at this year's Camp Bestival event.
Watch the video for 'Flutes' below: