* Indexes up: Dow 0.3 pct, S&P 0.2 pct, Nasdaq 0.1 pct

* Rally continues after Dow record on Tuesday

* Private sector employment gains by 198,000 in Feb

By Leah Schnurr

NEW YORK, March 6 (Reuters) - Wall Street resumed its climb into uncharted territory on Wednesday, with the Dow setting another intraday record as hiring by companies rose strongly last month.

The stock market rally this year has been helped by signs of a strengthening U.S. economy, continued support from the Federal Reserve and fairly attractive equity valuations compared with other assets.

"Stocks don't seem expensive here," said Paul Hogan, co-manager of the FAM Equity-Income Fund in Cobleskill, New York.

"All the headlines that were generated because of what happened yesterday with the Dow hitting new all-time highs, that makes more people take notice of the strength in the stock market. It may be bringing people in off the sidelines."

The slowly healing labor market has been one of the weaker spots of the recovery but data on Wednesday showed private sector hiring was surprisingly strong in February as companies added 198,000 employees.

It was an early look at the labor market two days ahead of the closely watched non-farm payroll report from the government on Friday, which is expected to show the economy created 160,000 jobs last month while the unemployment rate held at 7.9 percent.

The Dow Jones industrial average gained 45.61 points, or 0.32 percent, to 14,299.38. The Standard & Poor's 500 Index rose 2.90 points, or 0.19 percent, to 1,542.69. The Nasdaq Composite Index added 2.50 points, or 0.08 percent, to 3,226.63.

On Tuesday, the Dow ended at 14,253.77, breaking through October 2007's record close of 14,164.53. For the year, the Dow is up 9 percent. Shortly after trading began on Wednesday, the Dow punched through the previous session's intraday record, trading as high as 14,320.65.

The S&P has gained 8 percent in the year so far and is less than 2 percent below its record close. The larger S&P 1500 has already reached record highs, thanks to help from smaller-cap companies.

The Nasdaq fared worse than the other two indexes on Wednesday, weighed by Microsoft after the European Union fined the company 561 million euros ($731 million) for failing to offer users a choice of web browser. Microsoft was down 1.5 percent at $27.90

Financial shares gained with the KBW bank index up 0.7 percent. Bank of America climbed 2.2 percent to $11.80.

Staples tumbled 5.3 percent to $12.59 after reporting lower-than-expected quarterly revenue and forecasting weak earnings for the full year.