The Regolith x-ray Imaging Spectrometer (REXIS) is a coded-aperture soft x-ray imaging instrument on the OSIRIS-REx spacecraft to be launched in 2016. The spacecraft will fly to and orbit the near-Earth asteroid Bennu, while REXIS maps the elemental distribution on the asteroid using x-ray fluorescence. The detector consists of a 2x2 array of back-illuminated 1kX1k frame transfer CCDs with a flight heritage to Suzaku and Chandra. The back surface has a thing p+-doped layer deposited by molecular-beam epitaxy (MBE) for maximum quantum efficiency and energy resolution at low x-ray energies. The CCDs also feature an integrated optical-blocking filter (OBF) to suppress visible and near-infrared light. The OBF is an aluminum film deposited directly on the CCD back surface and is mechanically more robust and less absorptive of x-rays than the conventional free-standing aluminum-coated polymer films. The CCDs have charge transfer inefficiencies of less than 10^-6, and dark current of le-/pixel/second at the REXIS operating temperature of -60 degrees C. The resulting spectral resolution is 115 eV at 2 KeV. The extinction ratio of the filter is ~10^12 at 625 nm.