Bring salted water to a boil and add the pasta. Cook until al dente. Strain, reserving about a cup of the pasta cooking water, and return to the pot, but keep it OFF the heat. Stir in the cheese, but be careful to not let it clump up. Doing it in 3 smaller batches helps. Add in about half the pasta water and stir. Finally, add the yogurt and mix well. Stir in the chives.