We have used the Ultraviolet Imaging Telescope to obtain deep far-UV (1620 Angstrom), 40' diameter images of the prototypical metal-rich globular cluster 47 Tucanae. We find a population of about 20 hot (Teff > 9000 K) objects near or above the predicted UV luminosity of the hot horizontal branch (HB) and lying within two half-light radii of the cluster center. We believe these are normal hot HB or post-HB objects rather than interacting binaries or blue stragglers. IUE spectra of two are consistent with post-HB phases. These observations, and recent HST photometry of two other metal-rich clusters, demonstrate that populations with rich, cool HB's can nonetheless produce hot HB and post-HB stars. The cluster center also contains an unusual diffuse far-UV source which is more extended than its V-band light. It is possible that this is associated with an intracluster medium, for which there was earlier infrared and X-ray evidence, and is produced by C IV emission or scattered light from grains.