In a large bowl, cream butter and sugars until light and fluffy. Beat in eggs and vanilla. In another bowl, whisk flour, baking powder, salt and baking soda. Gradually beat into creamed mixture.
Divide dough into 2 portions. Stir chocolate into half of it. Divide white and chocolate portions in half. Wrap in plastic wrap and refrigerate 1 hour.
Roll out 1 portion of the chocolate and white into rectangle and cut each into 8 strips. Assemble the checkerboards. Roll out the other portions and assemble the pinwheels. Refrigerate.
Cut into 1/4 inch slices and bake at 375 degrees for 10 minutes, or just until set.