* Private firms add more jobs than expected in May

* Fed Governor Powell expects three rate hikes in 2017

* Palo Alto Networks rises after forecast beats expectations

* Dow up 0.57 pct, S&P 500 up 0.59 pct, Nasdaq up 0.58 pct (Updates to mid-afternoon, changes byline)

By Chuck Mikolajczak

NEW YORK, June 1 (Reuters) - U.S. stocks were higher on Thursday, with the S&P 500 and Nasdaq touching record highs, after a round of economic data suggested the economy was picking up speed.

The ADP private sector employment report showed that 253,000 jobs were added in May, well above the 185,000 jobs estimated by economists polled by Reuters.

The report could signal a strong government payrolls report on Friday that includes hiring in both public and private sectors and would cement expectations for a rate hike by the Federal Reserve in two weeks.

"I don’t think it locks in payrolls are going to be good, it’s more of payrolls aren’t going to be a disaster," said JJ Kinahan, chief market strategist at TD Ameritrade in Chicago.

Forecasts are for 185,000 non-farm payrolls created in May.

In addition to the ADP data, a separate report showed factory activity ticked up in May after two straight months of slowing.

San Francisco Federal Reserve Bank President John Williams said on Wednesday that while he sees three interest rate hikes this year as his baseline scenario, four rate increases would also be appropriate if the economy got an unexpected boost.

Fed Governor Jerome Powell, an influential policymaker, told CNBC that he expects three rate hikes this year.

Forecasts from Fed officials suggest that a median of two more hikes are planned before the end of the year.

"They are all singing the same tune. People’s money is saying this is very well baked into the market right now," said Kinhan.

Traders are currently pricing in a 93.6-percent chance of a quarter point rate hike at the central bank's June 13-14 meeting, according to Thomson Reuters data.

The Dow Jones Industrial Average rose 114.35 points, or 0.54 percent, to 21,123, the S&P 500 gained 14.07 points, or 0.58 percent, to 2,425.87 and the Nasdaq Composite added 35.88 points, or 0.58 percent, to 6,234.40.

Gains were broad, with each of the eleven major S&P sectors on the plus side, led by gains in materials, up 1.06 percent and healthcare, up 1.01 percent.

Deere's shares were up 2.2 percent at $125.2 after the farm and construction major said it would buy privately held German road construction company Wirtgen Group for $5.2 billion, including debt.

Hewlett Packard Enterprise dropped 6.4 percent to $17.62 as the biggest drag on the S&P 500 after the company reported a steep fall in quarterly revenue.

Palo Alto Networks jumped 16.0 percent to a more than four-month high of $139.97 after the cybersecurity company's profit forecast topped expectations.

Advancing issues outnumbered declining ones on the NYSE by a 4.42-to-1 ratio; on Nasdaq, a 3.38-to-1 ratio favored advancers.

The S&P 500 posted 28 new 52-week highs and 11 new lows; the Nasdaq Composite recorded 82 new highs and 70 new lows. (Reporting by Chuck Mikolajczak; Editing by Nick Zieminski)