Gamma-Ray Bursts (GRBs) have been proposed as a leading candidate for acceleration of ultra high-energy cosmic rays, which would be accompanied by emission of TeV neutrinos produced in proton-photon interactions during acceleration in the GRB fireball. Two analyses using data from two years of the IceCube detector produced no evidence for this neutrino emission, placing strong constraints on models of neutrino and cosmic-ray production in these sources.