Among the regular cast of characters who populate the pages of Hungary’s newspapers and magazines, the one whose fame is hardest to understand, in a country long proud of its disproportionate share of Olympic medals and Nobel Prizes, may be the man usually identified simply as the prime minister’s dentist.

Bela Batorfi’s rise to fame can be traced to the 2010 electoral victory of the conservative Fidesz party after eight years of Socialist Party dominance. Batorfi, then 41 years old, had a thriving practice in a posh residential corner of the capital with a clientele that included an impressive slice of the Budapest political elite. Among his longtime clients was the new prime minister, Viktor Orban, who had been his patient for almost 20 years. Orban quickly developed a reputation for ruthlessly punishing opponents and rewarding supporters, naming Fidesz loyalists to posts in the central bank and office of the chief prosecutor—departments that had been previously immune to partisan politics. “‘Orban is putting his people everywhere,’ is a constant lament in Budapest,” the Economist itself lamented early in his term. Even the man who tended to the first family’s teeth stood to benefit.

Batorfi is a specialist in oral surgery; he is also the face of one of the most unexpectedly shimmering sectors of Hungary’s post-communist economy. Between 2000 and 2008, the number of dentists in Hungary per capita increased by 56 percent. Hungary has more dentists per person than any other country, according to London journalist David Hancock, who in 2006 wrote a guide for British patients called The Complete Medical Tourist. “And since the country joined the European Union [in 2004] their fellow Europeans have had plenty to smile about, too, because prices are considerably cheaper there than in neighboring countries like Austria and Germany,” Hancock wrote.

By the time Orban became prime minister, medical tourism had become widely accepted by policymakers as unique tool for economic development. Its promise was almost magical: tourism for countries that had not been gifted with beaches or mountains, or had lacked the good sense millennia ago to preserve their abandoned stone structures for future sightseeing purposes.

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Unlike Orban, Batorfi’s patients from abroad typically saw him only once or twice, if ever. Much as luck had once placed a promising young parliamentarian into Batorfi’s dental chair years before the patient would make good in politics, a fortuitous connection had introduced Batorfi to the practice of medical tourism years before the phrase meant much of anything to anyone. In 2000, Batorfi told me, a Hungarian based in England had approached him with a proposal. If he could persuade Brits to take advantage of cheap Hungarian dental work, would the dentist share with him a cut of the new business?

Batorfi got a license to practice in the U.K. and rented an office in London. To his surprise, the patients started coming, adventurous types willing to confront the unfamiliar in search of prices that—even with all travel expenses included—typically fell below half of what they might pay in Bristol or Belfast. “In the beginning, that an English dentist would recommend a Hungarian dentist was unbelievable,” Batorfi marveled to me recently.

Recognizing that foreign customers would be most likely to travel for expensive treatments where they could realize the greatest savings, Batorfi got his masters in implantology, which includes some of oral surgery’s most complex procedures. Back in Budapest, he began setting his prices in British pounds and offering free chauffeur pickup at the airport. He bought advertisements in London media. “The proof of his work and competence are the more than 35,000 patients he has treated. Dr. Bartofi is honest and always ready to share his knowledge and expertise with his patients,” declared an ad Bartofi had placed in The Times. About a decade ago, Batorfi’s adviser Laszlo Szucs told me, Batorfi spent approximately $200,000 to acquire four of what his adviser Szucs calls “the Rolls-Royce of dental chairs.” Szucs claims that there are only four other existing versions of the same model, manufactured by the Japanese company Morita: one owned by Russian President Vladimir Putin, one by German Chancellor Angela Merkel, and two by a private Swedish clinic. (I could not confirm this independently.)

In 2010, medical tourism had already converted Bartofi’s business from a diverse family-oriented dental practice to a high-value oral-surgery outfit, and, with his patient and friend having become head of government, he and others close to him told me he began to contemplate whether the dominant market position he had assumed could be extrapolated into a type of national comparative advantage. A 2010 study by the country’s central tax bureau estimated that the 60,000 or so dental tourists who traveled to Hungary each year generated at least 65 billion forints (about $227 million) in revenue for dentists, with another 13 billion or so forints (about $45 million) in ancillary spending on hotels and restaurants. The sector had survived the 2009 global recession, and business showed little sign of slowing. After all, the peculiar dynamics that brought people to Batorfi’s London clinic for consultations and onward to Budapest for surgery—a British health system that made certain types of medical care scarce, or costly, or both—weren’t likely to yield anytime soon. “There are few things in which Hungary is in a leading position, and dental tourism is the one,” Batorfi says.

When the British dental profession started to push back at the Hungarian invasion of its home turf, it started with Batorfi himself. In 2011, he was informed that the British Dental Association had suspended his license to practice dentistry in the United Kingdom for one year. Charges of malpractice were based on the testimony of a patient who had, five years earlier, traveled to Budapest for implant surgery, and details of actual damages were sketchy.(Batorfi was alleged to have given insufficient advance information about the treatment plan and, after the patient expressed dissatisfaction with the procedure, had not responded to follow-up queries about options for corrective treatment.)

A month later, after an appeal, the suspension was rescinded, but not before the prime minister’s dentist had been elevated into a national symbol of Hungary’s ability to put wealthier countries on the defensive.

This helps account for Bartofi’s local celebrity: His frequent appearances in Hungarian media are most often in connection with political intrigue. When, in his second year in office, Orban invited dental businesses to bid for a series of government contracts, Batorfi entered and ultimately won everything for which he appeared to be eligible. Over the first four years of Orban’s administration, 3 billion forints in contracts and state aid—about $10 millionflowed from Hungary’s federal government to companies and trade associations under Bartofi’s influence. “Batorfi has been Orban’s dentist since 1992,” Szucs told the news magazine Heti Vilaggazdasag, defending his client’s right to bid. “Why wouldn’t he enter into a competition when any other business could compete?”

Announcing a major grant to the dental tourism sector at a Budapest conference in 2012, Orban called it “a worthy and good investment.” (In a country that has struggled to deliver quality health coverage to all its citizens, however, the fact that the most lucrative part of Hungarian health care was a gaudily extravagant sector that existed largely to serve foreigners’ vanities might look to some citizens like a failure of government.) The financial commitment was a bet that medical tourism was more than a fad—that what had very quickly shown Hungary to be effective at luring travelers to seek medical care wasn’t just the consequence of a few talented dentists emerging at the right time, or of Batorfi’s entrepreneurial instincts. Had Hungary made itself good at something that would last?

After officially winning the public contract to determine how that “worthy and good investment” would be spent, Batorfi turned to yet another one of his patients for help. Laszlo Szucs was a communications consultant based in Budapest whom Batorfi had informally asked for marketing advice in between visits to the dental chair for years. When Batorfi had first put Szucs on his payroll, in 2009, Szucs was in Napa Valley, working on a short documentary about a Croatian-American winemaker Mike Grgich, whose Chateau Montelena Chardonnay famously won the 1976 Judgment of Paris competition, establishing California wines as a formidable product with a distinct identity in the global marketplace. Szucs and Miklos Rozsa, a business consultant, began thinking about their product in similar terms.

“Our aim is,” Rozsa told me, “in Switzerland, you get chocolates and watches. In Hungary, you get dentistry.”

This article has been adapted from Sasha Issenberg’s new book, Outpatients: The Astonishing New World of Medical Tourism.