Beat butter in a medium mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add sugar and vanilla; beat until combined. Beat in egg. Beat in as much of the flour as you can with the mixer, stir in any remaining flour and 1 cup of the potato chips with a wooden spoon. Cover and chill dough for 2 to 3 hours or until easy to handle.
Shape dough into 1-1/2-inch balls. Roll balls in remaining crushed potato chips. Place balls 1 inch apart on an ungreased cookie sheet; flatten until about 1/4 inch thick. Bake in a 350 degree F oven about 12 minutes or until golden. Transfer to wire racks to cool. Makes about 20.