In a large pot, cook the pasta according to the package directions. Drain pasta.
In the same large pot, saute minced garlic in 1 tablespoon of butter. Saute over medium heat until the garlic is tender.
Stir in heavy cream, Parmesan cheese, drained pasta, and chicken. Blend until the cheese has melted. Season to taste with salt and pepper if desired.
Sprinkle with chives and add mozzarella cheese if desired. You can pop the pot into your oven set on broil if you want to brown the added mozzarella cheese for an added effect.