Reading the question about a future (the future) when non-automatic cars will be illegal, a moment sometimes called the automotive singularity, sparked the question in my mind about when the first story with driverless cars was written. There must have been dozens of stories with the driverless concept over the years.
I know Arthur C. Clarke tackled this in Imperial Earth, from 1976.
As the beautiful old car cruised in almost perfect silence under the guidance of it's automatic controls, Duncan tried to see something of the terrain through which she was passing. The spaceport was 50 km from the city - no one had yet invented a noiseless rocket - and the four-lane highway bore a surprising amount of traffic. Duncan could count at least 20 vehicles of different types and even though they were all moving in the same direction, the spectacle was somewhat alarming. "I hope all those other cars are on automatic," he said anxiously.
Washington looked a little shocked. "Of course," he said. "It's been a criminal offense for at least a hundred years to drive manually on a public highway. But we still have occasional psychopaths to kill themselves and other people..."
The big car was slowing down, it's computer brain sensing an exit ahead. Presently it peeled off from the parkway, then speeded up again along a narrow road whose surface rapidly disintegrated into a barely visible grass-covered track. Washington took the steering lever just a second before the END AUTO warning started to flash on the control panel.
But that's a late entry.
Isaac Asimov was earlier with his story Sally, in 1953. That's early, but I didn't think it was early enough.
I heard Sally coming up behind me and I put out my hand. She slid right into it and the feel of the hard, glossy enamel of her fender was warm in my palm.
"A nice automatobile," said Gellhorn.
That's one way of putting it. Sally was a 2045 convertible with a Hennis-Carleton positronic motor and an Armat chassis. She had the cleanest, finest lines I've ever seen on any model, bar none. For five years, she'd been my favorite, and I'd put everything into her I could dream up. In all that time, there'd never been a human being behind her wheel.
I did some more searching and I found what would seem to be a very early story, The Living Machine, by David H. Keller, from 1935.
"I want to show you something new in the way of an automobile." "Nothing new about this," laughed Babson, scornfully. "One of our best and most familiar models."
"How about the steering wheel?"
"Where is it?"
"I do not need one. Sit down and make yourself comfortable. Now watch me. We are going into traffic..."
That's relatively early into America's car culture, at least from today's perspective, and it might be the first. I haven't found anything earlier yet. But I wouldn't be surprised if it wasn't the first.
But was it? Does anyone know of an earlier story?