The spin wave dispersion in the planar 1D ferromagnet CsNiF3 has been measured by inelastic neutron scattering in an external field. The spin wave linewidths are found to decrease with increasing field and become resolution-limited for H>10 kG at 4.2K. At high fields, H>10 kG, both energies and intensities are found to follow linear spin wave theory. The analysis resolves a discrepancy between the anisotropy constants, A, derived earlier from spin-wave and susceptibility measurements, respectively. It turns out that a quantum correction is necessary in order to get consistent parameters. Two parameters namely the nearest-neighbour exchange, J/k=11.5+or-0.05K and A/k=8.9+or-0.2K, are needed to fully describe the system. The temperature dependence of the spin waves in an external field was also studied.