Put the butter, sugar and vanilla in a bowl. Beat with an electric mixer until creamy. Add the flour. Beat with the mixer for several minutes until a smooth dough forms.
Now press all the dough balls together. Roll them into a log. The log should be about 8 inches long. Chill the log in the refrigerator for 15 minutes.
Slice the log into pieces. Each slice should be about 1/4 inch thick. Put the slices on a cookie sheet and bake them for 10 minutes at 350°.