We report the first observational search for tau neutrinos from gamma ray bursts (GRBs) using one of the Ashra light collectors. The earth-skimming tau-neutrino technique of imaging Cherenkov tau showers was applied as a detection method. We set stringent upper limits on the tau-neutrino fluence in PeV-EeV region for 3780 s (between 2.83 and 1.78 hours before) and another 3780 s (between 21.2 and 22.2 hours after) surrounding GRB081203A triggered by the Swift satellite. This first search for PeV-EeV tau neutrino complements other experiments in energy range and methodology, and suggests the prologue of multi-particle astronomy with a precise determination of time and location.