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Despite a day-late arrival because of shipping problems, the first Chicago designers to exhibit in the Salone del Mobile, the world`s most prestigious furniture fair, eagerly unpacked their prototypes and settled into a booth at the sprawling Fiera Campionaria fairgrounds here.

Dubbed ”New Chicago Furniture: Made in Chicago, Made in Illinois,” the exhibit, organized by the Chicago Athenaeum gallery, includes pieces from Jeff Barnes, James Geier, Ioannis Karalias, Jordan Mozer, Ristomatti Ratia, Morlen Sinoway, Martin Spicuzza, Cal Spitzer and Allsteel, an Aurora-based furniture- maker.

The trip is part of an effort by the Athenaeum to promote Chicago as a design center.

”The Milan fair attracts a critical, high-buying audience as well as press,” said Christian Laine, the organization`s director, who coordinated the effort when last-minute space became available.

”We think it is important that Chicago be seen and represented in Milan.”

Envisioned as a cultural exhibit, the display has photos of the city along one wall of the makeshift booth, with brochures for visitors.

The four designers-Barnes, Spitzer, Karalias and Mozer-who made the trip to Italy with their prototypes were delighted to discover that a hitch in space allocation put them smack in the middle of a manufacturers` exhibition floor.

”To me it`s a great opportunity just to be here,” said Jeff Barnes when asked why he paid around $5,000 in travel expenses and hand-carried his steel ”mufff” stool from the United States to be a part of the fair. ”Visiting here and participating raises the level of your expectations.”

Noting that the Milanese are so wild about design that more than 50 publications on the subject are based here, Barnes said he wanted to see how his design compared to others.

”It`s not so much will your item sell as to show your idea, test it and be seen in context with so many others,” he said.

Besides, his wife, Bonnie, said, ”You can`t do this in America. You can`t go to a fair such as this for a week and have a booth. You have to pay for showrooms for an entire year.”

Cal Spitzer expressed concrete hopes for his trip.

”I`d love to meet a manufacturer,” he said, looking about for a producer willing to make in quantity the black marble and gold lacquered wood table he brought from his Evanston studio.

The early days of the exhibition brought mostly browsers and European press representatives, but the Chicagoans said they were pleased with this pioneering effort and would be happy to do it again next year.