Chicago's Alinea and New York's Eleven Madison Park, two of the nation's highly acclaimed restaurants, announced Tuesday they will be trading places for a week this fall.

Alinea and Eleven Madison Park, both holders of three Michelin stars, will trade chefs, kitchens and dining rooms, opening in essence pop-up restaurants in each other's space.

Alinea and chief Grant Achatz will be New York beginning Sept. 26 for five nights, and Eleven Madison Park, with chef Daniel Humm, will be in Chicago beginning Oct. 10.

In the most recent "World's 50 Best Restaurant" rankings, a survey of 800 international restaurateurs and food journalists, Eleven Madison Park was voted the 10th best restaurant in the world. Alinea was No. 7 in the rankings.

Achatz and partner Nick Kokonas have refused several offers to open an Alinea outside Chicago. The swap is a chance to present their cooking in New York without making a full-time commitment.

"I can't tell you how many chefs have said to me, `Yeah, you're a big fish in a small pond. The only reason you're so popular is because you're in the Midwest.' In a way, we're amped up," Achatz told the Chicago Tribune. "I want to introduce Alinea food to the jaded New Yorker. We're going to show New Yorkers what Chicago food is all about."

The collaboration is being called "21st Century Limited," a reference to the "20th Century Limited," a luxury passenger train that ran between Chicago and New York during the last century.

The idea was born last November at The Aviary, the cocktail lounge owned by Achatz and Kokonas, which played host to Eleven Madison Park's cookbook party, according to Achatz. He said it was a handshake deal, with both knowing it will be a tremendous amount of work.

Three days before the Sept. 26 opening night, Achatz and chef de cuisine Matt Chasseur will fly a dozen staffers to New York, and in a 72-hour crash course, train the Eleven Madison Park staff to replicate Alinea. The process repeats when Humm, general manager Will Guidara and their team arrive in Chicago on Oct. 7.

Foodies will pay a high price for meals at the restaurants -- $495 in both cities, not including tax and service.

Despite the expensive cover charge, both restaurants will lose money from the project.

"People sometimes don't understand why we're doing this when there isn't an economic benefit," Guidara said. "Sometimes we do what we do because we love doing it."