Cosmic rays have been observed on Earth with energies in excess of 1020 eV. Because cosmic rays are charged particles and are bent by galactic magnetic fields, the origin of these particles has remained a mystery. Gamma-ray bursts are one of a few astronomical sources containing an environment capable of accelerating charged particles to the energies observed. In addition, gamma-ray bursts are the leading candidate due to the fact that the total aggregate power observed in gamma-ray bursts and ultra high energy cosmic rays are the same order of magnitude. Neutrinos can only be created by hadronic interactions, so an observation of neutrinos in coincidence with a gamma-ray burst would provide compelling evidence that hadrons are accelerated in gamma-ray burst fireballs and hence the origin of cosmic rays. Using the IceCube Neutrino Observatory in its 40 string configuration, a stacked search was performed to look for the simultaneous occurrence of muon neutrinos with 117 gamma-ray bursts. This analysis is optimized on the assumption that order TeV neutrinos are produced in pγ interactions during the prompt phase of the GRB, when gamma-rays coexist with protons that are assumed to be the source of the observed extragalactic cosmic ray flux. With half the detector complete, this is the first analysis sensitive to the flux predicted by fireball phenomenology and the assumption that GRBs are the sources of the highest energy cosmic rays. No evidence for neutrino emission was found, placing a 90% CL upper fluence of 1.1 × 10-3 erg cm-2 in the energy range of 37 TeV - 2.4 PeV or 82% of the predicted fluence
