By Jack Pitcher

The Korean market frenzy is coming stateside.

SK Hynix, a South Korean chip maker and the latest global company to surpass $1 trillion in market value, kicked off the process for a U.S. listing on Monday that seeks to raise $28 billion in fresh capital.

The deal would rank among the biggest share sales in history, and make it much easier for American investors to access one of the hottest companies in the world's hottest stock market.

Surging demand for memory chips used by AI companies have turned SK Hynix and rival Samsung Electronics into dominant stocks on Korea's exchange. Shares of the two chip heavyweights are up 765% and 415% over the past year, respectively, though a lack of American depositary receipts for either company means few U.S. investors have participated in those gains.

Americans looking for Korean exposure have had to turn to roundabout methods, including buying shares in the Roundhill Memory exchange-traded fund, a concentrated bet on U.S. and Korean memory-chip stocks. Launched in April, the Roundhill fund became the fastest ETF in history to reach $20 billion in assets. In May, Interactive Brokers became the first major U.S. brokerage to open access to equities listed on the Korean exchange.

SK Hynix will begin trading in the U.S. on Friday, the company said in a regulatory filing. While its stock edged lower on Monday in Korea — selling new shares will dilute existing shareholders — chip makers gained broadly in the U.S. session, leading indexes higher.

Semiconductor companies Advanced Micro Devices, Qualcomm, and Broadcom were among the day's best-performing stocks. The tech-heavy Nasdaq composite added 1.1%, while the S&P 500 index was 0.7% higher. The Dow Jones Industrial Average rose 0.3%, or 156 points.

At Interactive Brokers, chip stocks and related ETFs have dominated the list of most actively traded securities in recent weeks, and Hynix's U.S. shares are likely to be a hit with customers after they list, said the company's chief strategist, Steve Sosnick.

Wall Street is carefully scrutinizing news and commentary surrounding AI companies' spending plans — which have been powering unprecedented profit growth for semiconductor companies — for any signs of a top. Since the PHLX Semiconductor Index peaked on June 22, it has posted a series of volatile drops and recoveries.

Brokerage data show individual investors have been stepping in to buy nearly every dip in shares of chip companies.

"Our customers are wedded to the strategy of buying dips, and that's worked very well for them. But if you do that indiscriminately, at some point, you can morph from dip-buyer to bag-holder," Sosnick said.

Dave Mazza, who helps run the smash-hit memory fund as chief executive of Roundhill Investments, remains bullish on chip stocks, pointing out that traditional valuation metrics like price/earnings still look reasonable for many of the companies because profits have grown so much.

"This industry is going through a sea change, and we think multiples will increase commensurate with the revenue growth these companies are beginning to produce," Mazza said.

Leveraged funds that amplify gains and losses on baskets of chip stocks or individual companies have been adding to the recent trading frenzy — and according to some traders, have been contributing to extremely high market volatility in Korea.

U.S. investors will soon have the chance to supercharge their Hynix bets, too: ProShares just announced that its new Ultra SK Hynix ETF, targeting twice the daily return of the company's ADR, will launch next week.

Leveraged funds tied to Micron Technology, Intel, and British semiconductor manufacturer Arm are all among the best-performing ETFs in the U.S. this year, with each posting gains of 400% or more.

Write to Jack Pitcher at jack.pitcher@wsj.com