* Nvidia shares above $1,000 mark after results

* Boeing sees negative free cash flow in 2024

* Live Nation tumbles on DOJ lawsuit

* Indexes down: Dow 1.4%, S&P 0.6%, Nasdaq 0.23%

May 23 (Reuters) - U.S. stocks fell on Thursday, even as a strong revenue forecast for Nvidia prompted a surge in its shares, but that was overshadowed by economic data showing inflation was still a concern.

Nvidia shares jumped more than 10% to climb above the $1,000 per share mark and helped boost the Nasdaq and S&P 500 to intraday records in the early stages of trading after the AI chip company forecast quarterly revenue above estimates and announced a stock split.

But stocks lost ground after economic data showed U.S. price pressures increased in May even as business activity accelerated and as lower weekly jobless claims indicated the labor market remains on firm footing.

"It may be speaks to the fact that people are now positioned for disappointing growth data, slower inflation data, rate cuts, and this morning... it caught people wrong footed," said Brian Nick Senior Investment Strategist at The Macro Institute in New York.

"Anything that looks like good news is still being greeted as bad news, which shows we're still in this sort of Fed relief rally period where the market's generally happy that interest rates have stopped going up, but the worst thing would be for interest rates to continue going up at this point."

The Dow Jones Industrial Average fell 556.66 points, or 1.40%, to 39,114.38, the S&P 500 lost 31.87 points, or 0.60%, to 5,275.14 and the Nasdaq Composite lost 38.11 points, or 0.23%, to 16,763.44.

The gains helped lift the S&P 500 tech index as the sole advancer among the 11 major S&P sectors on Thursday. But despite the gains in Nvidia, semiconductors on the whole were lower, with the PHLX semiconductor index down 0.21%.

The rally in equities to record highs this month has been fueled in part by AI optimism, a solid earnings season and renewed hopes for rate cuts by the Fed this year. Nvidia shares are up about 11% this year after surging roughly 240% in 2023.

Markets are now pricing in a 52.2% chance for a rate cut of at least 25 basis points (bps) in September, down from the nearly 67% a week ago, according to CME's FedWatch Tool.

The Dow was dragged lower in part by a tumble of more than 7% in Boeing after the U.S. planemaker forecast negative free cash flow in 2024 due to sluggish deliveries.

DuPont announced plans to split into three publicly traded companies. Shares of the U.S. conglomerate were edged up 0.34%, sharply off earlier highs.

Ticketmaster-owner Live Nation slumped 8.21% after the U.S. Justice Department and a group of 30 states and the District of Columbia Thursday sued to break up the concert promoter.

Declining issues outnumbered advancers for a 5.05-to-1 ratio on the NYSE and for a 3.59-to-1 ratio on the Nasdaq.

The S&P index recorded 33 new 52-week highs and seven new lows, while the Nasdaq recorded 132 new highs and 141 new lows.

(Reporting by Chuck Mikolajczak; Editing by Aurora Ellis)