  We study the spectral function, $S(k,\omega)$ for the spin-1, one dimensional
antiferromagnetic chain using a time-dependent density matrix renormalizaton
group (DMRG) numerical method. We develop methods for extrapolating the time
dependent correlation functions to larger times in order to enhance the
frequency resolution. The resulting spectral functions are impressively precise
and accurate. Our results confirm many qualitative expectations from non-linear
$\sigma$ model methods and test them quantitatively. The critical wave-vector
at which the single particle excitation emerges from the 2-particle continuum
is estimated to be $0.23\pi-0.24\pi$.
