(AMANDA Collaboration) Neutrino-based astronomy provides a new window on the most energetic processes in the universe. The discovery of high-energy (E = > = 1014 eV) muonic neutrinos (vmu) from gamma-ray bursts (GRBs) would confirm hadronic acceleration in the relativistic GRB-wind, validate the phenomenology of the canonical fireball model and possibly reveal an acceleration mechanism for the highest energy cosmic rays (CRs). The Antarctic Muon and Neutrino Detector Array (AMANDA) is the world's largest operational neutrino telescope with a PeV muon effective area (averaged over zenith angle) ~ 50,000 m2. AMANDA uses the natural ice at the geographic South Pole as a Cherenkov medium and has been successfully calibrated on the signal of atmospheric neutrinos (vatm). Contrary to previous diffuse searches, we describe an analysis based upon confronting AMANDA observations of individual GRBs, adequately modeled by fireball phenomenology, with the predictions of the canonical fireball model. The expected neutrino flux is directly derived from the fireball model description of the photon spectrum. The expected neutrino event rate is a function of the distribution of each individual burst in measured (or best-estimated) red shift. Strict spatio-temporal constraints (based upon satellite detection) and selection criteria (optimized for sensitivity) will be leveraged to realize a nearly background-free search.