  The low-lying excitations of the asymmetric $XXZ$ spin chain are derived
explicitly in the antiferromagnetic regime through the Bethe Ansatz. It is
found that a massless and conformal invariant phase with central charge $c=1$
is separated from a massive phase by a line on which the low-lying excitations
surprisingly scale with the lattice length as $\Delta E \sim N^{-\frac{1}{2}}$.
The mass gap vanishes with an exponent $\frac{1}{2}$ as one approaches the
massless phase. The connection with the asymmetric $6$--vertex model and some
physical consequences are discussed.
