An attempt has been made to observe an electric dipole moment of the neutron by performing a neutron-beam magnetic-resonance experiment with a strong electric field superimposed parallel to the uniform magnetic field. Significant limits of error of the measurement based upon probability considerations cannot be assigned because of systematic errors larger than those expected from statistics. The results are not consistent with any absolute value appreciably greater than ${10}^{\ensuremath{-}21} e$ cm and are consistent with other recent measurements.