On Earth near sunset, the Sun may cast "crepuscular rays" such that clouds near the horizon obscure the origin of light scattered in bright rays. In principle, active galactic nuclei (AGN) should be able to produce similar effects. Using new Hubble Space Telescope (HST) near-infrared and optical observations, we show that the active galaxy IC 5063 contains broad radial rays extending to ?11 kpc from the nucleus. We argue that the bright rays may arise from dusty scattering of continuum emission from the active nucleus, while the dark rays are due to shadowing near the nucleus, possibly by a warped torus. We also consider alternative AGN-related and stellar origins for the extended light. * Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. These observations are associated with programs #15444 and #15609.