Place the butter in a wide skillet over medium high heat. Once melted add the onions, sugar and allow to brown, stirring occasionally until browned on all sides. Now turn down the heat to medium and cover. Cook for another 15-20 minutes. Uncover, add the vinegar and simmer for another 5-10 minutes or until most of the liquid is gone and the onions are a brown and tender. Remove from the heat.
Meanwhile, cook the pasta according to instructions. When the pasta is done, strain and reserve about 1 cup of pasta water.
Add the yogurt into the pan with the onions and add a ladle of pasta water and stir in. Now add the cooked pasta and stir. If too thick add more pasta water and stir until desired consistency achieved.
Divide and plate, top with cheese and garnish with chives and serve.