In a large bowl, cream butter and sugars until light and fluffy. Beat in eggs and vanilla. Combine the flour, baking powder, salt and baking soda; gradually add to creamed mixture and mix well.
Divide dough into fourths. Tint one portion red and one portion green. Stir chocolate into another portion. Wrap chocolate and plain portions in plastic wrap; chill for 1 hour or until easy to handle.
For pinwheel cookies, divide red and green portions in half. Roll out each portion between waxed paper into a 9-in. x 6-in. rectangle. Refrigerate for 30 minutes.
Remove waxed paper. Place one green rectangle over a red rectangle. Roll up tightly jelly-roll style, starting with a long side; wrap in plastic wrap. Repeat. Chill for 2 hours or until firm.
For checkerboard cookies, divide plain and chocolate portions in half. Roll out each portion between waxed paper into a 6-in. x 4-in. rectangle. Cut each rectangle lengthwise into eight 1/2-in. strips.
Stack the strips in groups of four, alternating plain and chocolate strips and forming eight separate stacks. Form a four-stack block by alternating chocolate-topped and plain-topped stacks. Repeat. Press together gently. Wrap in plastic. Chill for at least 2 hours.
Unwrap and cut pinwheel and checkerboard dough into 1/4-in. slices. Place 1 inches apart on ungreased baking sheets. Bake at 375° for 9-11 minutes or until set. Remove to wire racks to cool. Yield: 6 dozen pinwheel and 4 dozen checkerboard cookies.