Could Parmesan cheese labels disappear from U.S. grocery store shelves?  They could, if the European Union has anything to say about it. 

The EU wants to keep names like Gorgonzola, Parmesan and Feta (which the EU described as "so closely connected to Greece as to be identified as an inherently Greek product") from being used on cheese made in the U.S., holding that American-made cheeses with European labels are lacking, and cut into not only the sales, but the reputations of their European counterparts. European Commission spokesman Roger Waite classified the matter as "an important issue for the EU," the Associated Press reports.

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The move isn't unprecedented. As recently as January, a British court ruled that New-York based Greek yogurt purveyor Chobani, couldn't market their yogurt as "Greek" in the United Kingdom because it was made in America. The lawsuit was brought by Fage, a Greek competitor. 

A group of U.S. senators from both sides of the aisle wrote to Michael Froman, a U.S. Trade Representative and Agriculture Secretary Tom Vilsack, saying the businesses owned by their constituents could be "unfairly restricted" if the proposal were to go through. 

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Representatives from the U.S. and EU are meeting in Brussels this week to continue to negotiate their Transatlantic Trade and Investment Partnership (TTIP) agreement. The EU's stance on importing genetically modified food from the United States is also a point of contention. 

The domestic cheese industry is worth $4 billion and cheese makers in the U.S. produced a record high in January, meeting the international demand of major importers like Mexico, South Korea and Japan.   

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