Cream butter and sugar; gradually add flour. Chill dough for at least one hour before shaping.
Using about a tablespoon of dough, roll into a 2 inch long finger. Bake at 325 for 15 minutes, or until lightly golden.
Melt chocolate chips in the microwave, starting at 45 seconds, and then stirring and repeating in 20 second intervals until completely melted. Dip one end of cooled cookies into chocolate and place on aluminum foil or waxed paper until chocolate is set.