Wash chard under running water and pat dry. Cut stems out of each leaf; slice stems into 1/4" pieces and place in a large bowl. Stack leaves and cut across in 1/2" strips; add to stems. Scrub potatoes and slice into 1/8" slices (6 to 7 cups); set aside about 1 1/2 cups to go on top of the casserole mixture, stir, and set aside.
Use about 3 tablespoons of the butter to generously grease a shallow 2 quart baking dish. Add remaining butter to chard mixture, stir and set aside.