It sounds like something out of a movie: An American Airlines pilot calls the control tower at Los Angeles International Airport to warn that his plane just flew past someone in midair — a person wearing a jet pack.

But the pilot really did give that warning last Sunday night, and it wasn’t laughed off. The FBI is investigating.

After all, there are a handful of companies around the world that make devices that power a single person up into the air.

Former Swiss Air Force pilot Yves Rossy has created a type of winged jet pack, which typically requires him to be hoisted into the sky by a helicopter or balloon in order to operate it. Another company, Zapata, has made something like a flying skateboard, which gives off a Marty McFly vibe.

JetPack Aviation Corp., based in Van Nuys, Calif., said it’s the only one to have developed a jet pack that can be worn like a backpack. Chief Executive David Mayman demonstrated it five years ago by flying around the Statue of Liberty.

So it’s not out of the question that someone could have been soaring above the airport last weekend, giving pilots a scare.

Mayman was quick to say that if a jet pack was involved, it wasn’t one of his. JetPack Aviation keeps its five packs locked down, he said, and they are not for sale. The company does offer flying lessons at $4,950 a pop, but he said students are attached to a wire and can’t stray too far.

None of the company’s competitors sell their products to consumers either, Mayman said.

The weekend incident “got us all wondering whether there’s been someone working in skunkworks on this,” he said, using a term for a secret project. Or maybe, he mused, the airline pilot saw some kind of electric-powered drone with a mannequin attached.

The fact remains: It’s very difficult to get access to a jet pack. If you accomplish that, though, it’s not hard to get permission to fly it.

The Federal Aviation Administration doesn’t issue licenses specifically for operating the devices. A jet pack could be operated as an ultralight vehicle if it meets weight, fuel capacity and speed requirements.

But it still wouldn’t be allowed to surprise officials by freewheeling over California’s biggest airport at night. Without FAA approval, ultralight vehicles can fly only during the day and are barred from flying over densely populated areas or in controlled airspace.

Jet packs that don’t meet the ultralight requirements could be issued a special experimental certificate, which would require a class of pilot certificate specific to the aircraft and have its own set of flight restrictions, the FAA said.

“If you want to do something that’s a thrill-seeking thing, then yes, you can fly one,” said Mike Hirschberg, executive director of the nonprofit Vertical Flight Society.

Selling to the general public at this point of time would create liability concerns.

“It’s so easy for someone to misuse one of these aircraft,” Mayman said. He doesn’t want to be on the hook if, say, a flier were to plow into a car or building.

Mayman said that he isn’t interested in selling his products to anyone but governments or government agencies, and that his company’s focus is on search-and-rescue applications.