We have carried out inelastic neutron scattering on CuC12 2N(C5D5), at T =1.2 K and at magnetic fields up to 70 kOe. The spin dynamics of this typical s =one-dimensional Heisen-2 berg antiferromagnet have previously been investigated at zero magnetic field by Endoh et al. , using neutron scattering. They observed a spectrum of magnetic excitations in close agreement with the spectrum of lowest excited states as calculated exactly by des Cloizeaux and Pearson (dCP). The marked asymmetry in the line shape of the neutron response previously observed is carefully reexamined and is shown to be a true effect, in agreement with several theoretical predictions. At high magnetic field, a broadening of the neutron response is observed, especially pronounced at the antiferromagnetic zone boundary, where the peak smears out at 70 kOe. For wave vectors near an antiferromagnetic Bragg point a decrease in the peak energy is observed for increasing field, lending qualitative support to the calculations of Ishimura and Shiba of the field dependence of the dCP states.