TSMC controls more than half the world's output of chips and supplies them for everything from Apple's iPhones to Nvidia's cutting-edge artificial intelligence hardware.

The company hit the threshold briefly after the opening bell in New York, but slipped lower in later trading.

TSMC's share price has increased this year by more than 85 percent.

The eye-watering valuation follows that of Nvidia, which makes AI chips and software and briefly became the world's most valuable company last summer.

The wild success of OpenAI's ChatGPT has sparked an AI gold rush, with demand surging around the world for the cutting-edge chips needed to train and run AI services.

TSMC dominates the global chip industry, and the bulk of its fabrication plants are based in Taiwan, a self-ruled island that is claimed by neighbouring China.

The hot demand for TSMC shares comes despite rising tensions with China.

Beijing has said it would not rule out the use of force to bring Taiwan under its control, and has in recent years ramped up pressure by sending in record-breaking numbers of warplanes and naval vessels around the island.