The sources of ultrahigh energy cosmic rays (CRs) are not yet known. However, the discovery of anisotropic CRs above 57 X 1018 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 57 X 1018 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 CR 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 57 X 1018 eV per year. Therefore, it is plausible that, over the course of several years, tens of CRs from a single source will be detected.