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The surface detector array of the Pierre Auger Observatory is sensitive to Earth-skimming tau neutrinos that interact in Earth’s crust. Tau leptons from ντ charged-current interactions can emerge and decay in the atmosphere to produce a nearly horizontal shower with a significant electromagnetic component. The data collected between 1 January 2004 and 31 August 2007 are used to place an upper limit on the diffuse flux of ντ at EeV energies. Assuming an Eν-2 differential energy spectrum the limit set at 90% C.L. is Eν-2dNντ/dEν<1.3 x 10-7 GeV cm-2s-1sr-1 in the energy range 2 x 1017 eV< Eν < 2 x 10M19 eV.