In a large mixing bowl, combine the sour cream, cream cheese, Parmesan, egg and herbs until the mixture it smooth. Fold in the onions, squash and chicken.
Transfer the squash mixture to a 9x13 baking dish. Arrange the cubed gruyere cheese over the casserole.
Melt the butter in a small bowl. Stir in the bread crumbs until coated. Sprinkle the breadcrumb mixture evenly over the chicken mixture.
Bake 65-70 minutes, until squash is fork tender. Allow the casserole to rest for 20 minutes before serving.