In a large bowl, cream together butter and sugar and add vanilla. Stir in flour and oats. Shape dough into 2 rolls, each 1-1/2" in diameter. Wrap well in waxed paper, twisting the ends to seal. Chill well, at least 2 hours, before baking.
When ready to bake, cut dough into 1/4" slices and place on ungreased cookie sheets. Top each with a chocolate star. Bake at 350 degrees for 10-12 minutes or until light golden brown. Remove to racks to cool.
You can freeze this dough, unbaked, for up to 2 months. Just slice and bake right out of the freezer, adding a few minutes to the baking time.
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