In quenched lattice QCD with standard Wilson fermions the quark propagator is computed very close to the chiral limit in the zero-temperature case. Starting from our experience with lattice QED we employ a modified statistical method in order to estimate reliably hadron masses. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(97-195) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman