Preheat oven to 350 degrees F. Place stick of butter in 13 x 9 baking dish, put in oven and melt.
Wash chicken breasts and pat dry. Wash potatoes, leaving the skins on, cut into quarters. Also pat these dry. Combine flour, salt and pepper in a medium sized bowl. Set aside.
When margarine is melted, carefully take out of oven and set baking pan on stove or other heat proof surface. Dredge the chicken and potatoes through the flour mixture, place into baking dish. Pour the entire bottle of Caesar salad dressing over the chicken and potatoes and cover with aluminum foil.
Bake 30 to 45 minutes, or until potatoes are fork tender. Then uncover and bake about 15 minutes more or until lightly browned on top. (I usually kick the oven up to about 375 degrees F at this point.)