Abstract : A thorough search of the sky exposed at the Pierre Auger Cosmic Ray Observatory reveals no statistically significant excess of events in any small solid angle that would be indicative of a flux of neutral particles from a discrete source. The search covers from -90° to +15° in declination using four different energy ranges above 1 EeV (1018 eV). The method used in this search is more sensitive to neutrons than to photons. The upper limit on a neutron flux is derived for a dense grid of directions for each of the four energy ranges. These results constrain scenarios for the production of ultrahigh energy cosmic rays in the Galaxy.