Set in a futuristic theme park, it finds the star seduced by the delights and distractions of modern life. Then slowly, like Katharine Ross in The Stepford Wives, she begins to realise something is terribly wrong with the (American) dream.
Adhering to Katy's new mantra of "purposeful pop", it's political without being polemic. Here are some of the key moments from the video, which you can watch in full on YouTube.
The futuristic theme park (actually Six Flags Magic Mountain in Valencia, California) is a metaphor for the infinite distractions of modern society - but in case that was too subtle, it has been renamed "Oblivia".
The guests are all taking selfies, eating giant sticks of candy floss (in the shape of mushroom clouds?) and crowding round an advert for "the greatest ride in the universe".
Everywhere you look, there are signs, icons and statues of a hamster. This will be important later.
The song's lyrics depict a world of repetition and ignorance, where technology renders us oblivious to people's real problems.
"Are we crazy? / Living our lives through a lens / Trapped in our white picket fence / Like ornaments / So comfortable, we're living in a bubble, bubble / So comfortable, we cannot see the trouble, trouble".
At first, Katy is awestruck, just like the other guests. But when she pricks her finger on a rose, there's a hint of trouble in paradise.
SCENE TWO: Roller coaster rodeo
Kudos to Katy, who manages to lip-sync her single perfectly while experiencing a G-force of 4.9 on a roller coaster.
Fact fans: The ride she's on is Full Throttle, which features the world's second largest vertical loop.
(We previously thought it was The New Revolution, a coaster that featured in the final scenes of cult comedy National Lampoon's Vacation, so thanks to the readers who spotted the mistake.)
SCENE THREE: Something sinister is afoot
As Katy loops the loop, we see another ride, which hoists tiny suburban houses towards the sky.
Suddenly, it malfunctions, and the houses plummet to the ground. A metaphor, perhaps, for the US housing crisis, where reckless lending left thousands of people homeless.
SCENE FOUR: The Big Reveal
The "greatest ride in the universe" turns out to be a treadmill. The guests aren't there to have fun - they're assets. Cogs in the machine. Literally hamsters on a wheel.
This image, coincidentally, makes sense of Chained to the Rhythm's lyric video, which saw Katy Perry cooking her pet hamster a hamburger. (We're applying a deliberately loose interpretation of the phrase "makes sense of" here.)
SCENE FIVE: "Inferno water"
The next scene takes place at a petrol station, where Katy is whisked off her feet by men in sailor costumes. (She might be making a serious political point but, hey, this is still a Katy Perry video.)
The pumps are supplying "inferno water" - a reference to the West's dependency on oil, but also to the looming crisis over the world's water supply, which some experts believe could lead to a war in Asia.
SCENE SIX: She's wide awake
As she sits down to watch a 3D movie, Katy notices a disturbing homogeneity amongst her fellow park guests who are, by now moving entirely in unison.
And while her message might be politically naive, it's commendable to see such a mainstream star prompting listeners to be more contemplative and engaged.
As a pop artist, it could cost her sales - but at least she's putting her money where her mouth is.