  We use the dynamical density matrix renormalization group technique to show
that the high-energy part of the spectrum of a S=1 Haldane chain, placed in a
strong external magnetic field $H$ exceeding the Haldane gap $\Delta$, contains
edge singularities, similar to those known to exist in the low-energy spectral
response. It is demonstrated that in the frequency range $\omega\gtrsim \Delta$
the longitudinal (with respect to the applied field) dynamical structure factor
is dominated by the power-law singularity
$S^{\parallel}(q=\pi,\omega)\propto(\omega-\omega_{0})^{-\alpha'}$. We study
the behavior of the high-energy edge exponent $\alpha'$ and the edge
$\omega_{0}$ as functions of the magnetic field. The existence of edge
singularities at high energies is directly related to the Tomonaga-Luttinger
liquid character of the ground state at $H>\Delta$ and is expected to be a
general feature of one-dimensional gapped spin systems in high magnetic fields.
