The painting is named "The Studio of Thomas Couture."
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It was purchased by UNC-Chapel Hill's Ackland Art Museum in the early 1970s.
Recently, the museum discovered that the painting had been stolen by the Nazis from a Jewish family during World War II.
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The painting was part of a collection of more than 450 works that belonged to Armand Isaac Dorville, who was a prominent French and Jewish lawyer and art collector.
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"It's always possible something you think you rightfully own may not be rightfully owned by your museum, and you have to keep your eyes and ears open to that possibility," said Katie Ziglar, the museum director. "It's a slim possibility and not very common but it can happen."
The family has gotten about 20 works of art back, but this is the first one from a museum in the United States.
"Though we are sad to see this painting leaving the museum's collection, the Ackland recognizes the historical injustice suffered by the Dorville family and its heirs by the crimes committed during the Nazi era," Ackland art curator Dana Cowen said. "Through the restitution of this work, we express our continued commitment to rectify such injustices of the past."