Snowboarder Lindsey Jacobellis hands out Chobani at the 2014 Sochi Winter Olympic Countdown in New York's Times Square on Oct. 29, 2013. Getty Images

An ongoing U.S.-Russia trade spat over dairy products is to blame for a shipment of 5,000 cups of Chobani yogurt that remain stuck in a New Jersey warehouse, but that hasn't stopped plenty of behind-the-scenes maneuvering to get the yogurt shipped to the Olympic village in Sochi for Team USA. A couple months ago, Chobani founder and CEO Hamdi Ulukaya agreed to airlift yogurt to Sochi for Team USA in to snack on during the games. The gesture dovetailed with new ads coupling Olympians and Chobani. The tagline: "It's one thing to sponsor an Olympian, it's another thing to be in their fridge."

Those ads apparently mattered very little to Russian authorities when the pallets of Chobani blueberry, strawberry, peach and plain Greek yogurt arrived late last week in Newark, N.J., from the company's production plants in Twin Falls, Idaho, and South Edmeston, N.Y.

They know how it impacts them and when they like to eat it. From that point alone, it's important for them to have it. Dan Benardot Professor of nutrition, Georgia State University, on US athletes

Now Sen. Chuck Schumer, D-N.Y., who originally championed the building of the Chobani plant in upstate New York, fired off a letter on Tuesday to Russian Ambassador Sergey Kislyak, unabashedly urging him to "permit a significant amount of Chobani Greek yogurt to enter Sochi so that the Olympic athletes can eat this protein-rich, New York-made food. … Russian authorities should get past 'nyet.'"

(Read more: Olympic TV announcers say Go Russia! Booooo USA!) On Thursday, the U.S. Dairy Export Council and the National Milk Producers Federation weighed in more specifically, calling on Russian authorities to end its country's three-year embargo of U.S. dairy products. The industry groups referred to a trade agreement that expired in 2010 and has been held up in negotiations since. On its website Thursday, the Russian Embassy stated that the nation's "Federal Veterinary and Phytosanitary Monitoring Service considers it important to explain that the importation of dairy and other products to [Russia] … is only possible when providing an approved veterinary certificate." That certificate, officially Form 28, involves the U.S. Department of Agriculture, which in an email statement to CNBC.com, said, in part: "We are working with our Russian counterparts to reach an acceptable solution that would allow this specific product to be shipped to the Olympic Village. We strongly urge Russia to help our U.S. company resolve this issue expeditiously so that our Olympic athletes have access to these products."