Abstract: Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85 degrees to +20 degrees, in an energy range from 10(17.3) eV to 10(18.5) eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm(-2) s(-1), and no celestial direction exceeds 0.25 eV cm(-2) s(-1). These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.