We have obtained new images of the protoplanetary disk orbiting TW Hya in visible, total intensity light with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST), using the newly commissioned BAR5 occulter. These HST/STIS observations achieved an inner working angle of similar to 0."2, or 11.7 au, probing the system at angular radii coincident with recent images of the disk obtained by ALMA and in polarized intensity near-infrared light. By comparing our new STIS images to those taken with STIS in 2000 and with NICMOS in 1998, 2004, and 2005, we demonstrate that TW Hya's azimuthal surface brightness asymmetry moves coherently in position angle. Between 50 au and 141 au we measure a constant angular velocity i...