Gary Sikka knew that it wouldn’t be easy to hire a top chef for his new Midtown restaurant, Mint — he didn’t realize that immigration laws would cause the process to take almost a year.

Mr. Sikka had tapped Rajan Safari, a renowned chef in India, but his restaurant had been open for 11 months before Mr. Safari walked in the door.

The city’s booming economy, combined with the phenomenon of globalization, has increased demand in New York for celebrity chefs from other countries. But American immigration laws are having a tough time keeping pace. Handcuffed by increasingly restrictive immigration policies, restaurant owners across the city are struggling to bring top international chefs to their kitchens. Getting a visa is especially tough for workers from China, India, Mexico, and the Philippines.

“There is a real hole in the system that prevents restaurants from hiring talented global workers,” an immigration lawyer with Cyrus D. Mehta & Associates, Elizabeth Reichard, said.

Under the current visa laws, there are no clear-cut provisions that apply to world-class chefs.

Mr. Safari served as the head chef at Bukhara in New Dehli, a restaurant annually ranked as one of the best in the world and regularly rated by Restaurant magazine in England as the best table in Asia.

Mr. Sikka’s attorneys advised him to petition for Mr. Safari as a candidate for a special visa given to “workers of extraordinary ability.”

American officials appear to have high standards for that classification.

“It would have to be someone like Wolfgang Puck,” a spokesman for the U.S. Citizenship and Immigration Services, Christopher Bentley, said. But even the Austrian-born Mr. Puck, the California cuisine genius whose name is now plastered on everything from frozen pizzas to airport fast-food counters, wasn’t a household name when he first came to America.

An alternative option for chefs is to apply for a temporary visa for workers with “specialty” skills. As a requirement, candidates must have a four-year bachelor degree or the equivalent training.

While a skilled chef could technically obtain this visa, known as an H-1B, it rarely occurs, according to Ms. Reichard. “The occupation of a chef is generally not considered a specialty even if they went to culinary school,” she said.

These visas are often snatched up first by other foreign professionals, including fashion models.

Immigration officials distribute only 65,000 of these “specialty” visas each year. The cap last year was met in just two months, leaving little room for restaurant owners to hire top chefs at other times during the year.

Congress is now debating whether to raise the limit on specialty visas, although the chef profession has been relegated to the sidelines. Companies in Silicon Valley are pushing lawmakers to permit more skilled international workers into the country to work in fields like information technology and computer programming, but some policy makers, in favor of the caps, want American workers to retain those jobs.

Several immigration experts say that chefs are pigeonholed out of the specialty visas because current policy gives precedence to other professionals.

Legislation introduced by Rep. Anthony Weiner, a Democrat who represents parts of Brooklyn and Queens, would free up about 1,000 specialty visas a year by making fashion models eligible for the classification reserved for “workers of extraordinary ability.”

Restaurants face other hurdles in securing “specialty visas” for their star chefs. Owners must prove that an American couldn’t bring similar expertise to the kitchen. That’s a difficult task, according the executive vice-president of the New York State Restaurant Association, Charles Hunt, who noted there are several world-renowned culinary schools in New York.

A chef fresh out of culinary school doesn’t always match up.

“There are no shortcuts to finding a Japanese trained chef,” the owner of the newly opened Rosanjin in Tribeca, Jungjin Park, said. He said, for example, that only a chef experienced in traditional Kaiseki technique could create Dashi, the bouillabaisse-like sauce that is the base of the Kyoto-style cuisine served at his restaurant.

The New York Post reported last month that the opening of Park Chinois, the highly anticipated Chinese restaurant in the Gramercy Park Hotel, is being delayed because the chef is having visa issues. The hotel declined to comment on the report.

The city’s high-end restaurants have limited influence in Washington for easing visa restrictions for top foreign chefs. They are often owned by groups of investors or small companies and don’t have the same pull as large chains.

The lobby group that represents the industry, the National Restaurant Association, is more focused on changing immigration laws to help service and labor workers, a spokeswoman, Sue Hensley, said.

Some international corporations use a loophole in the immigration law to bring employees who have a “specialized knowledge” of the business, a definition which could include braising beef at a Brazilian Churrascaria.

Employment based green cards are yet another vehicle that restaurants can use to bring a chef to the city, but green cards are extremely limited and applicants generally run into a multiyear waiting list, experts say. There are also caps that specifically target Chinese, Indian, Mexican, and Filipino workers.

The visa restrictions have had an impact on quality, the owner of the Shun Lee Palace, Michael Tong, said, pointing to what he called the decline of good Chinese food in the city over the past 30 years.

“It’s difficult for top Chinese chefs to get to America, and with a booming Chinese economy they don’t need to leave,” he said.