Deep CCD and near infrared imaging and photometry of flat spectrum radio sources from the 1 Jy sample show that nearly all members have an optical or infrared identification with a brightness closely proportional to the radio flux density (in agreement with identification programs for other flat spectrum radio samples). There is one outstanding exception, which is far fainter than expected from this proportionality, and two additional objects which are very faint galaxies but whose nuclei may also be very faint. Because the other very faint optical identifications are obscured or have very red continua, it is possible that these three sources are just extreme examples of the same behavior; on the other hand, they might represent an optically (and infrared) quiet type of quasar. Because no other flat spectrum sources seem to be truly optical-infrared quiet, the latter possibility would imply discovery of a new emission mechanism or source geometry for quasars. Deep ISO imaging of these sources at 11.5 microns can tell if they are intrinsically faint in the infrared as well as in the optical.