Shang Skipper is running out of time to solve a problem he never expected. In a few weeks, Skipper plans to open Del Frisco’s Grille in Chestnut Hill, and despite the state’s relatively high unemployment rate, he can’t find enough workers to fill well-paying jobs with benefits at the chain restaurant.

Over the past month, Skipper has scoured college campuses, hosted a booth at a Cambridge job fair, and slipped into after-hours hangouts popular with bar and restaurant workers to woo prospective hires. Despite those recruiting efforts, he said, 30 positions remain open.

“It’s surprising that we see these unemployment numbers and still aren’t getting enough applicants,” he said.

But at many upscale restaurants in the Boston area, that seems to be the case. Even with 250,000 people out of work in Massachusetts, restaurant owners say they have vacancies for positions ranging from part-time host to experienced sous chef.

Economists cite several factors for the job-employee gap: a mismatch between the part-time jobs available and the full-time work most people need, a lack of skilled chefs, and restaurateurs who are being too choosy.

The hiring situation is dramatically different from just a few years ago. Back then, restaurants that managed to make it through the recession had their pick of top-notch workers from competitors that went out of business or were forced to cut staff.

With the improving economy and a rise in consumer confidence, people are eating out more frequently. That has led to an influx of new establishments. Bars and restaurants in the state added more than 15,000 employees from 2010 to 2012, three times the growth rate between 2008 and 2010, according to the Census Bureau.

“It’s become a much tighter and more competitive work environment,” said Bob Luz, president of the Massachusetts Restaurant Association. “The economy is on the road to recovery, and the talent pool is thinner.”

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