Pour in the heavy cream and bring to a simmer. Stir in the softened cream cheese until smooth.
Add the shredded mozzarella and grated Parmesan, stirring until melted. Return the cooked chicken to the skillet. Add the cooked pasta and toss to coat.
Notes
Refrigerate leftovers in an airtight container for up to 3 days. It can also be frozen for up to 2 months.