In the tug of war over Taiwan, chips play a decisive role.

A hundred miles of typhoon-swept sea from China’s southeastern coast, a string of colossal factories in Taiwan churns out the most important electronic devices on Earth.

The tiny, intricate chips that give life to phones, computers, cars, satellites and almost everything else with a power source are at the center of the economic contest between the United States and China, a rivalry that is shaping the future of technology worldwide.

The issue loomed in the backdrop of Speaker Nancy Pelosi’s visit to the island democracy on Wednesday, as she spoke with the head of one of the biggest power players in chips, Taiwan Semiconductor Manufacturing Company.

Today’s cutting-edge chips are mostly made in Taiwan, where the two powers are entangled in a geopolitical tug of war over the island’s future. In Washington, Beijing and Taipei, diplomatic and military calculations are interlinked with concerns about the supply chains without which the modern world might come to a halt.

The United States wants to safeguard its leadership in semiconductors, a technology that Americans pioneered in the last century and built into the industry that gave Silicon Valley its name. China desperately wants to catch up, both to help move its economy away from low-end manufacturing and to upgrade its military capabilities.

Tech companies on both sides of the Pacific rely heavily on Taiwan Semiconductor Manufacturing Company, the island’s biggest silicon foundry, to craft the high-performance chips that render graphics in video games and give smartphones their smarts. They also guide missiles and analyze oceans of military data. That has turned T.S.M.C., whose name is obscure to most consumers, into a vital strategic asset for both Washington and Beijing.

Taiwanese leaders have maneuvered for decades in the narrow space between American and Chinese interests. Now, they face an even more precarious balancing act.

Many Taiwanese businesses — T.S.M.C. included — rely on China for their livelihoods, even if they support the island’s president in standing up to Beijing’s pugilistic behavior. As T.S.M.C. works on a new Arizona plant, the company is also expanding its facilities in Nanjing, China.

As a way to try to counter China, Congress recently passed a $280 billion bill designed to bolster America’s manufacturing and technological edge, particularly the semiconductor industry. Ms. Pelosi, after meeting with the Taiwanese president on Wednesday, also said that she was hopeful for a trade pact with Taiwan.

Dieter Ernst, a senior fellow at the Center for International Governance Innovation who studies the semiconductor industry, said of Taiwan’s leaders, “Right now, they’re moving very much toward the U.S.” But from the perspective of the Taiwanese economy and most Taiwanese companies, he said, “they need to retain a link — and hopefully as close as possible a link — with China.”