  The surface detector array of the Pierre Auger Observatory is sensitive to
Earth-skimming tau-neutrinos $\nu_\tau$ that interact in the Earth's crust. Tau
leptons from $\nu_\tau$ 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 is used to place an upper limit on the diffuse flux of $\nu_\tau$
at EeV energies. Assuming an $E_\nu^{-2}$ differential energy spectrum the
limit set at 90 % C.L. is $E_\nu^{2} \mathrm{d}N_{\nu_\tau}/\mathrm{d}E_{\nu} <
1.3 \times 10^{-7}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$ in the energy range
$2\times10^{17} \mathrm{eV} < E_\nu < 2\times10^{19}$ eV.
