The most dependable hourly chime ever made costs about fifteen dollars and runs for years on a single battery. The Casio F-91W, the little plastic digital watch that has outlived every trend since the eighties, beeps once at the top of every hour. It is a tiny sound with a strange power: it tells you where you are in the day without asking you to look at anything. My iPhone, a computer several million times more capable, cannot do this out of the box.
There is no setting for this on the iPhone
You can search Settings for "chime" and find nothing. The Clock app only rings at fixed alarm times. This is not an oversight so much as a policy. iOS is strict about apps making noise in the background whenever they please, which on balance is a blessing, and it means an hourly chime has to arrive some other way.
The Apple Watch secretly does it
If you wear an Apple Watch, you already own the nicest hourly chime Apple makes, and it is hidden where nobody looks. On the watch, open Settings, then Accessibility, then Chimes. Turn it on and you can pick a schedule (hourly, or every thirty or fifteen minutes) and a sound. There are two: Bells, and a short birdsong. With the watch on silent you get a few gentle taps on the wrist instead. It is the best feature Apple has never advertised, filed under Accessibility like a secret.
You can also set it up from the iPhone: open the Watch app, then Accessibility, then Chimes.
On the iPhone itself, you need an app
Because of the background noise policy, chime apps deliver their sound through notifications, the same channel as a text message. Done well, this is indistinguishable from a real chime. I make one of these apps, Hourlybird, and its bird sounds are a direct homage to the Apple Watch ones, because the watch chime is what I missed on days I forgot to wear it. It is free, it handles hydration and stretch reminders too, and it has a pause button for meetings. Other apps do this as well, and I wrote an honest comparison of them in a field guide to the hourly chime apps.
The do-it-yourself route
The Shortcuts app can play a sound at a fixed time through a personal automation. To make that hourly, you build one automation per hour, by hand, one at a time. I include this for the kind of person who enjoys that. You know who you are.
Hourly sound used to be public infrastructure. Church bells, factory whistles, the radio pips: whole towns agreed on what time it was because something above the rooftops said so. That layer of shared time is mostly gone now, and I miss it, which is probably why I ended up carrying a bell tower in my pocket.