Cook pasta according to package directions. Meanwhile, in a large saucepan, add cream and butter; cook until butter is melted. Stir until smooth. Add cheese; cook and stir until cheese is melted. Rinse and drain pasta; add to cheese mixture. Cover and keep warm.
In a large skillet, saute onion and garlic in 3 tablespoons oil until onion is tender. Add squash; cook until tender. Add 1 teaspoon of salt and pepper; remove and keep warm.
Add remaining oil to skillet; cook chicken with herbs and remaining salt until juices run clear. Place pasta on a serving platter; top with chicken and squash. Yield: 8 servings.