  The sources of ultra-high energy cosmic rays are not yet known. However, the
discovery of anisotropic cosmic rays above 57x10^18 eV by the Pierre Auger
Observatory suggests that a direct source detection may soon be possible. The
near-future prospects for such a measurement are heavily dependent on the flux
of the brightest source. In this work, we show that the flux of the brightest
source above 57x10^18 eV is expected to comprise 10% or more of the total flux
if two general conditions are true. The conditions are: 1.) the source objects
are associated with galaxies other than the Milky Way and its closest
neighbors, and 2.) the cosmic ray particles are protons or heavy nuclei such as
iron and the Greisen-Zatsepin-Kuz'min effect is occurring. The Pierre Auger
Observatory collects approximately 23 events above 57x10^18 eV per year.
Therefore, it is plausible that, over the course of several years, tens of
cosmic rays from a single source will be detected.
