The recent observations of superconductivity at temperatures up to 55K in compounds containing layers of iron arsenide have revealed a new class of high temperature superconductors that show striking similarities to the more familiar cuprates. In both series of compounds, the onset of superconductivity is associated with the suppression of magnetic order by doping holes and/or electrons into the band leading to theories in which magnetic fluctuations are either responsible for or strongly coupled to the superconducting order parameter. In the cuprates, theories of magnetic pairing have been invoked to explain the observation of a resonant magnetic excitation that scales in energy with the superconducting energy gap and is suppressed above the superconducting transition temperature, Tc. Such resonant excitations have been shown by inelastic neutron scattering to be a universal feature of the cuprate superconductors, and have even been observed in heavy fermion superconductors with much lower transition temperatures. In this paper, we show neutron scattering evidence of a resonant excitation in Ba0.6K0.4Fe2As2, which is a superconductor below 38K, at the momentum transfer associated with magnetic order in the undoped compound, BaFe2As2, and at an energy transfer that is consistent with scaling in other strongly correlated electron superconductors. As in the cuprates, the peak disappears at Tc providing the first experimental confirmation of a strong coupling of the magnetic fluctuation spectrum to the superconducting order parameter in the new iron arsenide superconductors.