The company, which has branched out from Greek-style yogurt, will invest more than $1 billion in the plant in the city of Rome.

Chobani got its start in 2005 in the middle of New York State, in a decades-old Kraft factory that had become defunct, initially hiring just a few of its workers to produce Greek-style yogurt.

Two decades later, the company — now one of the nation’s biggest producers of dairy products — is opening another plant nearby, to significantly more fanfare and economic impact.

Chobani and New York State announced on Tuesday that the company would open a million-square-foot factory in Rome, N.Y., costing at least $1.2 billion and able to make one billion pounds of dairy products a year. Company executives describe the plant, which they reckon will be the biggest dairy factory in the United States, as a much-needed expansion to fulfill growing demand.

“We’ve been growing, but that has

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