The first dedicated search for ultra-high energy (UHE) tau neutrinos of
astrophysical origin was performed using the IceCube detector in its 22-string
configuration with an instrumented volume of roughly 0.25 km^3. The search also
had sensitivity to UHE electron and muon neutrinos. After application of all
selection criteria to approximately 200 live-days of data, we expect a
background of 0.60 +/- 0.19 (stat.) $^{+0.56}_{-0.58}$ (syst.) events and
observe three events, which after inspection emerge as being compatible with
background but are kept in the final sample. Therefore, we set an upper limit
on neutrinos of all-flavors from UHE astrophysical sources at 90% CL of $E^{2}
\Phi(\nu_{x}) < 16.3 * 10^-8 GeV cm^-2 sr^-1 s^-1 over an estimated primary
neutrino energy range of 340 TeV to 200 PeV.
