Cut potatoes in half length wise. Boil until tender, but not so tender they fall apart. Cut into cubes and place in bottom of 13x9 dish.
Cut 1/2 stick of butter and place around on top of potatoes. Mix together cream of chicken, sour cream, and shredded cheese. Spread over potatoes. Melt 1/2 stick of butter and mix with crushed crackers. Spread on top of mixture in dish.