IceCube has become the first neutrino telescope with a sensitivity below the TeV neutrino flux predicted from gamma-ray bursts if gamma-ray bursts are responsible for the observed cosmic-ray flux above 10(18) eV. Two separate analyses using the half-complete IceCube detector, one a dedicated search for neutrinos from p gamma interactions in the prompt phase of the gamma-ray burst fireball and the other a generic search for any neutrino emission from these sources over a wide range of energies and emission times, produced no evidence for neutrino emission, excluding prevailing models at 90% confidence.