We describe SPIDER, a balloon-borne instrument to map the polarization of the millimeter-wave sky with degree angular resolution. Spider consists of six monochromatic refracting telescopes, each illuminating a focal plane of large-format antenna-coupled bolometer arrays. A total of 2,624 superconducting transition-edge sensors are distributed among three observing bands centered at 90, 150, and 280 GHz. A cold half-wave plate at the aperture of each telescope modulates the polarization of incoming light to control systematics. SPIDER's first flight will be a 20-30-day Antarctic balloon campaign in December 2011. This flight will map ~8% of the sky to achieve unprecedented sensitivity to the polarization signature of the gravitational wave background predicted by inflationary cosmology. The SPIDER mission will also serve as a proving ground for these detector technologies in preparation for a future satellite mission.