  We study the dynamic spin correlation function of a spin one
antiferromagnetic chain with easy-plane single-ion anisotropy. We use exact
diagonalization by the Lancz\H os method for chains of lengths up to N=16
spins. We show that a single-mode approximation is an excellent description of
the dynamical properties. A variational calculation allows us to clarify the
nature of the excitations. The existence of a two-particle continuum near zero
wavevector is clearly seen both in finite-size effects and in the dynamical
structure factor. The recent neutron scattering experiments on the
quasi-one-dimensional antiferromagnet NENP are fully explained by our results.
