Beat butter, sugar & vanilla in large bowl with mixer until fluffy. With mixer on low, gradually beat in flour just til blended. Remove half of the dough to a sheet of waxed paper. Shape into a ball & divide in half. Add cocoa to dough remaining in bowl & beat on low until well blended. Divide in half. With lightly floured hands, roll each of the 4 pieces (start with the 2 without cocoa) into a rope 11" long. On a sheet of waxed paper, put a chocolate rope & a plain rope side by side & touching.Top the chocolate rope with the remaining plain & the plain one with the chocolate one to form a checkerboard pattern. Lightly press down on log, then turn a log a quarter turn & lightly press down again. Repeat until log is squared off & 12" long. Wrap airtight & freeze 8 hours or until hard. Let dough stand at room temp about 20 minutes. Heat oven to 350. Have ungreased cookie sheets ready. Cut dough in 60 slices. Place 1" apart on ungreased sheets.
Bake 8-10 minutes until edges of plain dough are golden. Remove to wire rack to cool. Store airtight up to 2 weeks or freeze.