Taiwan Semiconductor Manufacturing Company, which is manufacturing the world’s most advanced microchips, conducts business on the island of Taiwan, dead center in one of the most geopolitically volatile places on the planet.

That makes people in Washington very nervous. TSMC dominates the semiconductor industry; it’s a company that the United States can’t do without, 80 miles off the coast of China.

The U.S. government has appropriated tens of billions of dollars to strengthen America’s own semiconductor sector and help fund TSMC’s nascent operations in the United States, far from China, which has never renounced the use of force to absorb Taiwan.

But TSMC has invested billions of its own over nearly four decades growing deep roots in Taiwan. There, it employs a small army of engineers, research and development scientists, technicians and production workers in the exquisitely complex task of producing chips, etching electronic pathways smaller than a cell on plates of silicon.

It would be exceedingly difficult to replicate what TSMC has built in Taiwan, said Mark Liu, chairman of TSMC. Developing and producing the company’s most cutting-edge chips at a rapid pace requires a huge effort, he said, as many as 3,000 research scientists for one generation of the technology.

“We cannot put it anyplace else,” he said.

TSMC has embarked on a global expansion, with two factories under construction in the United States and one in Japan, as well as a possible facility in Germany. It’s part of the company’s strategy to address the calls by U.S. officials to reduce America’s reliance on chips made in Taiwan.

That makes the 68-year-old Mr. Liu, who holds a doctoral degree in electronic engineering and computer science, as much a diplomat as a scientist and an executive. He joined TSMC 30 years ago after stints at Intel and Bell Labs, rose through the ranks and today runs the $500 billion company with its chief executive and vice chairman, C.C. Wei.

In late June, when he spoke to The New York Times at TSMC’s offices in the northern Taiwan city of Hsinchu, he had just returned from a trip to the United States, which he said he visits roughly every three months.

“We have a pretty good relationship across Congress, the Commerce Department, the White House. I think they know us,” he said.

It’s a bit of an understatement. Initial efforts to court TSMC and bring its production facilities to the United States led to the creation of the CHIPS and Science Act, a program to expand the U.S. semiconductor industry. So complete is TSMC’s lead in the industry that there is no obvious second option for all it does. Any clash over Taiwan — where the vast majority of its manufacturing happens — would stop the flow of the TSMC microchips, putting a deep freeze on the technology industry and, in turn, the global economy.

As befits a company obsessed with protecting its hard-won technological lead, TSMC’s offices feel more like a secret government research facility than a Silicon Valley campus.

Next to turnstiles where workers swipe their badges, a sign notes that five people have been fired since 2010 for breaking the company’s strict internal security rules. One offense included improperly changing the subject line of an email in a reply. Outside phones are banned. Although policies have recently loosened up, employees tell stories of eating lunch in the parking lot so they can access their personal phones.

Windowless buildings the size of aircraft hangars operate 24 hours a day to produce microchips, the tiny brains inside smartphones, airplanes, supercomputers and just about anything else electronic.

Political leaders in the United States and its allies in trade battles with China have pushed TSMC to build production facilities outside Taiwan. And China has tried hard to compete with TSMC, using everything from hacks and intellectual property theft to hundreds of billions of dollars in investment.

As the United States has sought to hinder China’s advances in semiconductor technology, TSMC has been caught in the middle. In 2020, TSMC cut off orders to the Chinese tech powerhouse Huawei, which was TSMC’s second-largest customer at the time. Mr. Liu said TSMC, because it is reliant on American technology, had no choice.

“It’s understandable, but support or not, we have no say,” he said.

Mr. Liu rejected the idea of the “silicon shield”: that Taiwan’s chip-making prowess deters military action by China and brings support from the United States. Both need Taiwan’s chips.

“China will not invade Taiwan because of semiconductors. China will not not invade Taiwan because of semiconductors,” he said. “It is really up to the U.S. and China: How do they maintain the status quo, which both sides want?”

TSMC has made a $40 billion investment in Arizona to build two factories to produce chips that are one or two generations behind its most advanced ones. The company is expected to submit its application for CHIPS Act subsidies this month, Mr. Liu said.

The Arizona plants have been slow going, and the company has deployed hundreds of Taiwanese technicians to expedite the process. Last month it pushed back the expected start date by a year to 2025, and it has faced high costs and managerial challenges. Internal tensions over cultural differences have surfaced between TSMC and American workers.

And doubts loom over whether American companies will be willing to pay the likely premium required for chips made in Arizona, where TSMC’s construction costs alone could be at least four times higher than they are in Taiwan. Mr. Liu said he had told the U.S. government that it needed to offer American companies incentives, beyond the $52 billion in subsidies in the CHIPS Act, to buy American-made chips.

“Otherwise, it will be limited,” he said. “It will come to limits pretty quickly. So that is on the table. But I don’t think we have a solution yet.” The Commerce Department, in charge of handling CHIPS Act incentives, declined to comment on specific companies.

In 2018, Mr. Liu said, the Commerce Department under President Donald J. Trump urged the company to invest in the United States. And several TSMC clients privately approached Mr. Liu at an industry conference and expressed the need for it to establish a U.S. manufacturing presence. Mr. Liu sensed the landscape was shifting.

“I thought maybe it’s time for TSMC to go a little bit global, because I know our technology is leading today, but what about in the future?” he said.

Before long, the Trump administration’s State Department, citing national security grounds, started courting TSMC, emphasizing the role of advanced chips in military gear like F-35 fighter jets. Keith Krach, under secretary of state for economic growth, energy and the environment, arranged a phone call between Mr. Liu, Secretary of State Mike Pompeo and Commerce Secretary Wilbur Ross.

Mr. Liu recalled that Mr. Krach said TSMC was needed to help “catalyze” the American semiconductor industry.

“That for me is also important because the U.S. is where 65 percent of our customers reside,” Mr. Liu said. “They have different needs, and we also have opportunities.”