WEST HOLLYWOOD, Calif. — The problem with stardom, most any star will tell you, is you can’t turn it off anymore. Certain protocols used to apply when it came to sightings of famous folk in public. But that was in the bygone days of the Brown Derby or Chasen’s, about a billion “creepshots” ago.

Now, of course, it is next to impossible for people like Jennifer Aniston or Justin Timberlake to do the boringly normal stuff the rest of us take for granted. And that realization was at the core of an idea the hotelier Jeffrey Klein had for a personal second act.

After more than a decade operating the celebrity petting zoo that is Sunset Tower Hotel and its now-storied Tower Bar, Mr. Klein understood better than most that the one craving that famous people cannot satisfy is to get their anonymity back.

“Privacy is the new luxury,” Mr. Klein said one chilly recent morning, a week after he opened the doors on his latest project, a private club whose membership is largely composed of strangers you know by name.

It has been 15 years since Mr. Klein and his partners paid $18 million for the Sunset Tower, a faded Art Deco relic on a stretch of Sunset Strip that, although now booming, had fallen into funky desuetude. Against most odds and all prevailing wisdom, he soon established it and its Tower Bar restaurant as essential landmarks of the new Hollywood.

The Tower Bar, in particular, quickly evolved into the preferred watering hole of studio moguls, literary agents, fashion designers, power brokers and A-list movie stars, who prized Mr. Klein’s ability to reconcile the paradox that the famous experience the same giddiness we all do when exposed to others of their kind. Unlike ordinary mortals, though, they also yearn to recapture the privacy whose loss is the price tag of modern celebrity.

With no fixed ambition to do so, Mr. Klein eased into the role of social Hollywood’s de facto gatekeeper, “sort of like a cross between Billy Haines and George Cukor with a little Perle Mesta,” as the screenwriter Jon Robin Baitz said (referring to a film star turned decorator, an Oscar-winning director and the Washington hostess who inspired “Call Me Madam,” the 1950 Irving Berlin musical).

And for the past 13 years, ever since the Sunset Tower was “painstakingly restored to its Art Deco glory,” as The New York Times once noted, nobody got a power table at its cozy wood-paneled restaurant without going through Mr. Klein’s right hand man, Dimitri Dimitrov, 68: a Macedonian immigrant and career maître d’ himself renowned for an uncanny ability to diagram the fluctuations of Hollywood power, and equally for courtesy so mannered as to evoke Kabuki.

For years, Vanity Fair held its Oscars night party at his hotel, along with the more stellar one given by the powerful talent agency CAA. And for years, Mr. Klein was approached by investors eager to replicate the Sunset Tower’s success. “I could have slapped my name on a thousand things and rolled out new properties," he said. “But I didn’t want to do just another hotel.”

Instead Mr. Klein pursued a challenge equal to that first presented by the Sunset Tower. “I like dumps, and I like places with ghosts,” he said. Both, as it happened, were to be found under his nose at a druggie, clothing-optional motel complex blocks away from Sunset Tower in West Hollywood, a cluster of bungalows erected in the late 19th century as housing for workers laying railway lines to the coast.

The Jolt of Soho House

Not everyone would have detected in this collection of listing frame structures the potential for a private club that would make getting into Tower Bar seem almost as easy as grabbing a booth at IHOP.

But Mr. Klein had long nurtured a dream of recreating in Los Angeles a members-only gathering place on the order of Annabel’s, a London nightclub founded in 1963 in what had been a coal cellar by the aristocratic British entrepreneur Mark Birley and distinguished by a clientele that, over the years, included royals and Frank Sinatra, Aristotle Onassis and Kate Moss.

Not coincidentally, this interest coincided with a growing trend in Los Angeles, as elsewhere, for people to come together in upscale public settings not unlike social versions of a gated community.

Clubs are far from new in Los Angeles, of course, their long history likely beginning with the “gentlemen-only” California Club, which opened over a livery stable in 1887, followed eight years later with establishment of the staid Jonathan Club, whose headquarters still occupy almost a block of prime real estate in the city’s downtown (with another outpost on an unrivaled stretch of beach in Santa Monica).

But it was Soho House that jolted the social landscape of Los Angeles with its opening nearly 10 years ago in a glass-box building along Sunset Boulevard just shy of Beverly Hills.

“They invited me and John to be founding members and I said no,” Mr. Klein said, referring to his husband, John Goldwyn, a producer and scion of the film family. “I thought I would never want to be a member of a private club,” he added — or even, as Groucho Marx once said “any club that will have me as a member.”

That perspective shifted, Mr. Klein said, when membership in Soho House boomed and the agents, actors, producers, publicists and studio executives that had long patronized his restaurant and hotel began clamoring to get in. “It pricked up my ears to see how successful it was," Mr. Klein said.

Rather than a membership roster drawn from a relatively broad swath of the local population, however, Mr. Klein envisioned for the San Vicente Bungalows a more tightly edited group of those representing the ecosystem he knows best: one composed principally of apex predators.

“There’s nothing elite about it,” Mr. Klein told this reporter, as though testing for plausibility an assertion that fails to square with the fact that the advisory committee at San Vicente Bungalows is reputed to include some of the most prominent names in the art, fashion and entertainment industries. Annual dues, for that matter, are $4,200 for members over 35.

It was a chilly afternoon and Mr. Klein, 48, was seated in the forecourt of his new nine-bungalow complex dressed in a tan Boglioli blazer, a Brunello Cucinelli button-down and a rumpled pair of Acne jeans. The San Vicente club was fresh from a six-year renovation estimated to have cost $50 million — nearly $2 million of it allocated for gardens in which transplanted, century-old California pepper trees now shade lattice walls of espaliered kumquats — and there were glitches.

The power was dead in three electrical sockets in the club’s cozy living room, where the screenwriter Robert Harling (“Steel Magnolias”) sat in a corner tapping on an iPad. Vintage glass candy jars of peanut M&Ms were arranged on a console, but not precisely to Mr. Klein’s liking. A waitress attired in an aproned uniform from Mercatores, a Milanese livery shop, had set a lunch table backward, knife to the left and fork on the right.

Consulting his phone, Mr. Klein noted that a member who was asked to resign from the club after staging a tipsy dining-room tantrum was bombarding him with text messages: “She’s begging to get back in.”

Though by his own admission a “control freak,” Mr. Klein’s public face is one of affability and disarming bonhomie; he is perhaps unique as a businessman in his deployment of “I love you” as an all-purpose term of greeting and farewell.

“Growing up, I always had to compensate with personality for this lack of intelligence I thought I had because I was severely dyslexic,” he said. “I was brought up with everyone telling me I was stupid. But I always had confidence in this ability to connect with people and connect them to each other.”

The club of his fantasies, Mr. Klein said, was intended less as a new power matrix two miles from the one he already owns than as a democratic town square. What he envisioned at the San Vicente Bungalows, he said, was “an oasis” not unlike the storied Hollywood residential complex called Garden of Allah and made famous by inhabitants like Somerset Maugham, Ginger Rogers and F. Scott Fitzgerald. “I wanted this to be a place where a street artist can sit next to Spielberg.”

Glance around, though, and no street artists are to be found. There is, however, Mr. Dimitrov — who followed Mr. Klein here from the Tower Bar, his ostentatious hospitableness intact though his striped suits traded for knit Armani blazers and sneakers from Comme des Garçons — escorting Lorne Michaels to a table in the candlelit dining room.

A Bronfman in the Bougainvillea

The dominant mood of the San Vicente Bungalows club is snug and domestic. With its pool room hung with stridently colorful works selected by the Swiss artist Urs Fischer (a member); its oak-paneled living room designed by the English decorator Rita Konig as homage to Bunny Mellon’s Virginia library; its lush garden created over two years by Lisa Zeder, it resembles a Hollywood dream house out of the movies, as one member said.

“It’s actually kind of a cross between a glorious English cottage, Bugsy Siegel’s hide-out and Bemelmans bar,” said Mr. Baitz, the screenwriter (and club member).

In its design, the club’s interior courtyard allows for clear sightlines on almost every entrance and exit. And here, in fact, much like Tracy Lord skipping down the front steps of her Main Line mansion in “The Philadelphia Story” comes Hannah Bronfman, the D.J. heiress, descending from one of the club’s nine private bedrooms to duck beneath a bower of pink bougainvillea. And there, hunched with a script in a rattan cafe chair, sits Armie Hammer. And here is John Mayer, feet shod in Visvims and propped on a coffee table.

While elsewhere in town, van loads of tourists are being carted around to view houses once inhabited by movie stars gone and long forgotten, at San Vicente Bungalows the live ones disport themselves.

“I know, there is sort of an eye roll about the exclusivity” aspect of belonging to the club, Tracee Ellis Ross, the actress and comedian, said later by telephone. “It feels privileged and all of that. But at the same time there is this real need in Los Angeles for a place where you can go and be a private person and take off the celebrity part of yourself at the door.”

As if to underscore that notion, members and guests at the club sign a code-of-conduct contract upon entry and surrender their phones to desk attendants dressed in piped rowing blazers. The phones are returned to them, of course, but only after the camera lens has been covered with a sticker bearing the logo of the club.

“Believe me, there are people at the club far more recognizable than me,” Mr. Hammer said last week by telephone from home, where he was hanging out with his young daughter, Harper Grace. “Even for me, though, it’s great that you don’t have to worry about someone walking up and taking a selfie, or being pestered in any way.”

In Mr. Klein’s world, the paparazzi that routinely bribe servers and slip weekly updated price lists to parking valets for celebrity tipoffs may be a necessary evil. Instagram is the enemy. “We live in this connected world where no one is really connected,” he said, adding that if his experience at Sunset Tower alerted him to anything it was a need to create a “safe zone” for those people whose faces beam out at us from the covers of the tabloids.

“There actually are not that many celebrities in the world," D.A. Wallach, the musician and tech entrepreneur (and club member), said recently. “Part of what Jeff is good at is creating a community and environment for this rarefied group.”

In a dream factory like Hollywood, where the business meeting is the dominant form of social intercourse and transience a defining state, community can sometimes seem like an anomalous concept. “L.A. lacks a coherent, cohesive culture of gathering places,” Mr. Baitz said flatly. “It just does.”

What is never in short supply is the hypnotic pull those on the inside exert on the rest of us and the sense that life would far better if you could only join the club. And that is Mr. Klein's fundamental proposition at both the Tower Bar and his San Vicente Bungalows.

“What makes L.A. so interesting is that it has always been this city of immigrants with this fantasy about what their own lives could become here," Mr. Wallach said. “There’s a recursive element in the way Jeff exports this idea of the culture of Hollywood even to Hollywood itself. San Vicente Bungalows is a throwback to something. But what?”