(CBS) — Should babies be banned from restaurants that provide fine dining?

It’s a question a world-famous Chicago chef is asking on Twitter after a weekend incident involving a baby.

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CBS 2’s Mike Parker reports.

It was Saturday night in the city’s most expensive; most stylish; some say, most magnificent restaurant — Alinea. It’s a place where atmosphere and taste and the experience are to be savored.

Suddenly, a crying baby. Famed chef Grant Achatz takes action, then tweets.

The family is asked to leave. The chef wonders: Did he do the right thing?

John and Heather Aitken have experienced the “experience” at Alinea.

“You pay dearly for that, and yeah, we love babies, we had one. But boy: Not the right place for it,” he says.

But father John Crist says: “Having two little girls myself, I feel like if you are running a restaurant that is that well known, you need to find a way to make all your customers welcome.”

Late Monday, somebody using the moniker “Alinea Baby” responded to the chef with its own tweet: “I’m a baby who likes fine food, fine drinks, and crying.”

The so-called Alinea baby also wrote a restaurant review on the Yelp website complaining about a lack of “sippy cup” refills.

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The flap became a supernova on the Twitterverse.