"They were very romantic with one another," a source tells PEOPLE of Sean Penn and his mystery date

By Michael Miller and Ana Calderone
Updated March 18, 2016 06:50 PM
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Credit: Kevork Djansezian/Getty

Is there a new woman in Sean Penn’s life?

The Gunman actor was spotted kissing a 20-something mystery blonde while on a romantic date night at Chicago Cut Steakhouse on Sunday.

“He came in with no reservation so he was not pretentious or trying to set it up or making sure he was incognito – he literally walked right in,” a source tells PEOPLE.

Penn’s companion, “a beautiful young blonde in her 20s,” sat with the actor “in plain sight over in the window seat,” which the source notes “looks out onto the Chicago River, so it’s a pretty romantic view.”

The pair ordered cocktails before dinner, which consisted of “oysters, a sea bass and a steak, and then they both had dessert and hot tea.” Throughout the meal, the source notes, “they were very romantic with one another.”

After finishing dinner, Penn posed for a photograph with the restaurant’s hostess, and when diners started asking for their own pictures, Penn and his date “dashed out the door.”

The Oscar winner, who recently made headlines with his controversial interview with Mexican drug lord Joaqu n “El Chapo” Guzmén, split with his former girlfriend Charlize Theron last year.

Meanwhile, the actor’s ex-wife and “good friendMadonna expressed her lasting affection for Penn at a charity event in January. “I want to say Sean, I love you, from the moment that I laid eyes on you,” the singer said in a speech to Penn while attending the Help Haiti Home gala in Beverly Hills, California.