* US private sector adds 215,000 jobs in Dec -ADP

* U.S. jobless claims rise in holiday-distorted week

* Fed to release minutes from FOMC Dec meeting

* Futures dip: S&P 2.3 pts, Dow 20 pts, Nasdaq 1 pt

By Angela Moon

NEW YORK, Jan 3 (Reuters) - Wall Street was set for a slightly lower open on Thursday, as investors lock in gains after a rally Wednesday, which was spurred by a deal by U.S. lawmakers to avert a "fiscal cliff" of austerity measures that had been due to kick in this year.

Earlier losses in U.S. stock index futures Thursday were capped by better-than-expected data that showed U.S. private-sector employers added 215,000 jobs in December. That was well above economists' expectations for a gain of 133,000 jobs, according to a Reuters survey.

"The underlying economy has momentum, and the employment data confirms that. The political issues in Washington counter the momentum we're seeing in the economy, but you might see still equities grind higher today on this," said John Brady, managing director at R.J. O'Brien & Associates in Chicago.

A separate report showed the number of Americans filing new claims for unemployment benefits rose last week, but the data was too distorted by year-end holidays to offer a clear read of labor market conditions.

S&P 500 futures fell 2.3 points and were below fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures lost 20 points, while Nasdaq 100 futures dipped 1.00 point.

Wall Street began the new year Wednesday with a rally and their best performance in more than a year, sparked by a last-minute deal in Washington to avert a fiscal cliff of automatic massive tax hikes and spending cuts that, in the worst-case scenario, would have hurt the nation's economic growth.

The minutes of the Federal Reserve's policy meeting last month will be released at 2:00 p.m. EST (1900 GMT). The minutes will give details on the discussions of the Federal Open Market Committee's Dec. 11-12 meeting.

U.S. retailer Costco Wholesale Corp reported a better-than-expected 9 percent rise in December sales at stores open at least a year, mainly helped by an additional sales day in the reporting period. Costco shares were flat in premarket trading.

Gap Inc will buy women's fashion boutique Intermix Inc for $130 million to enter the luxury clothes market, the Wall Street Journal reported. The stock surged 4.9 percent to $32.90 in premarket trading.

Family Dollar Stores Inc reported a lower-than-expected quarterly profit as its emphasis on selling more everyday items like cigarettes and soft drinks put pressure on margins. The stock fell 8 percent to $58.89 in premarket trading.

Growth in China's increasingly important services sector accelerated in December at its fastest pace in four months, adding to signs of a modest year-end revival in the world's second-largest economy.