  We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with
Hamiltonian $H=-\sum_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1} +\Delta
S^{(3)}_xS^{(3)}_{x+1}$, is given by $\Delta-1$ for all $\Delta\geq 1$. This is
the gap in the spectrum of the infinite chain in any of its ground states, the
translation invariant ones as well as the kink ground states, which contain an
interface between an {\it up} and a {\it down} region. In particular, this
shows that the lowest magnon energy is not affected by the presence of a domain
wall. This surprising fact is a consequence of the $SU_q(2)$ quantum group
symmetry of the model.
