Cook squash and onions in boiling salted water until tender. Drain and mash them with 1/2 cup butter or margarine. Stir in sour cream, grated carrot and cream of chicken soup. Set aside.
Melt remaining 1/2 cup butter and stir it into the stuffing mix. Pour half of the stuffing mix into the bottom of a 9X13 glass baking pan. Pour the squash mixture over the top of the mixture, and the rest of the stuffing mix on top of the squash.
Bake for 30 minutes, until golden brown and bubbly.