Cook pasta in salted water until al dente. Reserve ½ cup pasta water and drain.
Heat olive oil in a large skillet over medium-high heat. Add chicken, season with salt, pepper, and Italian seasoning, and cook until golden and cooked through. Remove and set aside.
In the same skillet, add onion and cook until soft. Stir in garlic and cook until fragrant.
Lower heat and add cream. Stir gently and heat without boiling.
Add mozzarella and Parmesan cheese, stirring until melted and smooth.
Return chicken to the pan and add cooked pasta. Toss to coat evenly.
Add reserved pasta water as needed to loosen the sauce.
Taste, adjust seasoning, and serve warm.