When the door of the garage in a rural Connecticut town rolled open one day last month, the morning sun revealed a historically important — and long-stored — Ferrari.

The white 1966 365 P Berlinetta Speciale by Pininfarina is startling in many ways, with three-across seating — the driver sits in the center — being its most unusual feature and the reason for its nickname of Tre Posti. Add to that its provenance as a show car, its long-term ownership by a key figure in Ferrari’s success and a midmounted V12 engine.

Examining the low-slung 365 P were David Gooding, whose California-based Gooding & Company will auction it in California on Aug. 17, a sale that is one of the many events surrounding the Pebble Beach Concours d’Élégance on the Monterey Peninsula; Luigi Chinetti, the car’s owner and son of Ferrari’s first United States importer; and Wayne Carini, host of the “Chasing Classic Cars” TV show on Velocity.

Mr. Carini is also the owner of F40 Motorsports in Portland, Conn. His company repainted the 365 P many years ago, and he has long been its caretaker.

The aluminum-body 365 P has some design points in common with Ferrari’s 246 GT Dino, including the fender shape, a slim grille opening and a convex back window with bold buttresses extending rearward. Compared with a Dino, though, the 365 P impresses as the more subtle and well-proportioned shape.

“This is one of the most significant vehicles we’ve ever offered,” Mr. Gooding said. “It’s totally original and the last bespoke car that Pininfarina built for a client.” He estimates a winning bid of as much as $30 million.

The 365 P is built on a racecar chassis designed for Le Mans and the North American Racing Team of the senior Chinetti, who died in 1994. It was an opportunity for Pininfarina to show that a competition-proven midengine layout could work in a road car.

“And grand prix drivers sat in the middle,” Mr. Gooding said.

Before its delivery to Chinetti, the car was displayed at the 1966 Paris auto show and at the Earls Court Motor Show in London. A period British newsreel about that show declared, “Hand signals are definitely out,” referring to the long reach to the window.

Chinetti sold it to a New York businessman, who didn’t like the car, according to Gooding’s research; the next owner, Jan de Vroom, an adventurer and sometime racecar driver, sold it back to Chinetti in 1969.

A second, quite different, 365 road car was built and delivered to Giovanni Agnelli, who became the head of Fiat in 1966.

“There was very little similarity,” Mr. Chinetti, who is known as Coco, said. “The proportions were different and the engine and chassis as well.” Mr. Chinetti described driving with the steering wheel in the middle as “very natural — there’s no offside.”

So why is he selling the car now? “There comes a time when the responsibility of ownership is too great,” he said. “It’s too significant a car.”

An odometer reading of 7,900 kilometers (about 4,900 miles) suggests that rarity and value have prevented daily commuter duty. But Mr. Carini, who has occupied that central seat, said the Ferrari was “wonderful to drive.”

The 365 P was not drivable during my visit, though it will be by the time of the auction. I was at least able to try out the unusual driving position. The car sits very low, so climbing in over the passenger seat requires the agility of a younger driver. Once I was settled in the cabin, it felt comfortable, and the gated 5-speed shifter was well placed.

An owner with an active social life might find this Ferrari, with seating for two companions at the same time, ideal. But Mr. Chinetti, who says the 365 P is his favorite car — and had been his father’s too — was clear on that point. “I never drove this car with a girlfriend. It was mostly two-seaters and one girl.”