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* May PPI falls unexpectedly, weekly jobless claims at 10-month high

* Broadcom soars after FY forecast raise on AI chips strength

* Tesla up as Musk says shareholders to approve his $56 bln pay package

* Nasdaq briefly touches fresh intraday high

* Indexes: Dow down 0.71%, S&P down 0.14%, Nasdaq up 0.10%

June 13 (Reuters) - The S&P 500 and the Dow indexes slipped on Thursday as investors weighed hawkish Federal Reserve projections against data signaling cooling inflation, though strength in chip stocks supported the Nasdaq.

Nasdaq component Broadcom soared 12.2% to hit a record high after the chipmaker raised its forecast for revenue from semiconductors used in artificial intelligence (AI) technology. It also announced a 10-for-1 forward stock split.

AI chip leader Nvidia rose 2.8%, pushing the Philadelphia SE Semiconductor Index 1% higher to an all-time peak.

The information technology sector also hit a record high, but nine of the other 11 major S&P 500 sectors were in the red.

The S&P 500's pullback came a day after the index notched its third consecutive record close.

A Labor Department report showed the U.S. producer price index (PPI) unexpectedly fell 0.2% month-on-month in May, compared with a 0.1% increase expected by economists polled by Reuters.

Separately, the number of Americans filing new claims for unemployment benefits increased to a 10-month high last week.

Markets lifted bets on a September start to rate cuts to nearly 68% from 60% before the data, according to the CME's FedWatch tool.

That was despite policymakers projecting only one rate cut this year in the Fed's policy statement on Wednesday, despite softer-than-expected U.S. consumer inflation data.

"For the markets, there's some uncertainty - yesterday's dot plot was hawkish because they went from three rate cuts to one rate cut predicted in 2024," said Sonu Varghese, global macro strategist at the Carson Group.

"Markets are reflecting that volatility," Varghese said, but added he still sees a September rate cut on the table.

UBS Global Research said it now expects the Fed to cut interest rates in December instead of September, while Goldman Sachs and Morgan Stanley continue to expect the first cut in September.

At 12:03 a.m. ET, the Dow Jones Industrial Average was down 281.43 points, or 0.73%, at 38,430.78, the S&P 500 was down 8.78 points, or 0.16%, at 5,412.25, and the Nasdaq Composite was up 18.07 points, or 0.10%, at 17,626.51.

Amid the optimism, questions also remained over whether the economy was slowing too quickly, with an index of economically sensitive small-cap stocks slipping 1.4% after rising more than 2.4% across the last two sessions.

Tesla leapt 3.8% after Elon Musk said company shareholders were voting to approve his $56 billion pay package and to move the electric-vehicle maker's legal home to Texas.

Apple was flat after overtaking Microsoft as the world's most valuable company earlier in the week.

Virgin Galactic plunged 14.7% a day after announcing a 1-for-20 reverse stock split.

Declining issues outnumbered advancers for a 2.39-to-1 ratio on the NYSE. Declining issues outnumbered advancers for a 2.35-to-1 ratio on the Nasdaq.

The S&P index recorded 13 new 52-week highs and 8 new lows, while the Nasdaq recorded 43 new highs and 97 new lows.

(Reporting by Lisa Mattackal and Johann M Cherian in Bengaluru; Editing by Devika Syamnath)