Begin cooking the pasta to al dente.
While the pasta is cooking heat a large clean pan to medium-low heat and add the butter and garlic.
Cook the garlic until golden (about 2 minutes).
Add the cream and cheese and bring to a simmer. The sauce will begin to thicken after a couple of minutes of simmering.
Add the al dente pasta to the alfredo sauce and mix or toss to coat. If the pasta is too dry add some of the reserved pasta water, a bit at a time, to get a perfect consistency.
Remove the pan from the heat.
Season with salt and pepper to taste and add the parsley.
Cut the chicken into slices and top on individual plates or mix it straight into the pasta in the pan.
Serve with more grated Parmigiano Reggiano on the side.