The Labor Department says weekly applications fell by 30,000 to the lowest level since February 2008. The four-week average, a less volatile measure, dropped by 11,500 to 364,000, a six-month low.
Applications are a proxy for layoffs. When they consistently drop below 375,000, it suggests that hiring is strong enough to lower the unemployment rate.
The decline adds to other evidence that hiring is improving. Last week's jobs report showed the unemployment rate fell to 7.8 percent, the first time it has fallen below 8 percent since January 2009.
Stocks opened higher after the better-than-expected job numbers.