Pete Johnson discovered Viniv in 2010 when a friend in a cigar club told him he was making his own wine in Bordeaux. “I said: ‘What do you mean you’re making wine in Bordeaux? That’s what I want to do.’”

Mr. Johnson, 45, a custom cigar maker and entrepreneur in Los Angeles, has made five vintages since then, including Bone Ami, in homage to his Rottweiler, and Tatouage French for tattoo, in homage to his ornately inked forearms. (Duke of Juice is also his.) He figures he has spent more than $150,000 making wines at Viniv, not including airfare and hotels.

“I am making the best possible wine for my palate,” he said. “This isn’t your two-buck Chuck.”

There are other Bordeaux chateaus that try to give visitors a sense of ownership. Typically they allow visitors to adopt a plot of vines or personalize their bottles.

Image A label from a personalized wine.

Viniv caters to clients who are willing to commit the time, travel and expense — and break a Bordeaux taboo. Mr. Bolger offers customers three grape varietals from 13 different vineyards, allowing them to mix a cabernet sauvignon from Pauillac with a merlot from Pomerol. For the wine establishment of Bordeaux, blending grapes from different appellations is the vintner’s equivalent of fantasy football, or eugenics.

“I recently had an older farmer who refused to sell me his vines,” Mr. Bolger said. But he also said rejections were rare because Viniv wines are not commercially sold; they are savored by their creators.

“This isn’t a gimmick,” Mr. Bolger said. “It’s a real and entirely different way of producing fine wine.” And make a splash. “I think it’s fun at dinner parties to pour my own wine for friends instead of something banal,” Mr. Boucraut explained.