Natural (such as lunar) occultations have long been used to study sources on small angular scales, while coronographs have been used to study high contrast sources. We propose launching the Big Occulting Steerable Satellite (BOSS), a large steerable occulting satellite to combine both of these techniques. BOSS will have several advantages over standard occulting bodies. BOSS would block all but about 4e-5 of the light at 1 micron in the region of interest around the star for planet detections. Because the occultation occurs outside the telescope, scattering inside the telescope does not degrade this performance. BOSS could be combined with a space telescope at the Earth-Sun L2 point to yield very long integration times, in excess of 3000 seconds. If placed in Earth orbit, integration times of 160--1600 seconds can be achieved from most major telescope sites for objects in over 90% of the sky. Applications for BOSS include direct imaging of planets around nearby stars. Planets separated by as little as 0.1--0.25 arcseconds from the star they orbit could be seen down to a relative intensity as little as 1e-9 around a magnitude 8 (or brighter) star. Other applications include ultra-high resolution imaging of compound sources, such as microlensed stars and quasars, down to a resolution as little as 0.1 milliarcseconds.