No reason has been publicly given for the closures.
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The chain, which opened its first location in 1983 in Little Tokyo, was sold last year to an investment firm, Food Management Partners, according to the Los Angeles Times.
It had locations around Southern California, including Torrance, Gardena, Little Tokyo and other cities.
Customers and fans are mourning the closure, saying if they knew it was shutting down, they would have had a chance to grab one last meal.
"Everyone was so passionate about the food and we all worked together as a family. It's been a very rough day for all of us, but we all are still hanging in there," one former employee tweeted.
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Fans at one location even went so far as to leave flowers and candles as a makeshift memorial, with social media showing signs reading "RIP Curry House" and "The day the Curry died."