  A continuum limit of the non-Hermitian spin-1/2 chain, conjectured recently
to belong to the universality class of the noisy Burgers or, equivalently,
Kardar-Parisi-Zhang equation, is obtained and analyzed. The Galilean invariance
of the Burgers equation is explicitly realized in the operator algebra. In the
quasi-classical limit we find nonlinear soliton excitations exhibiting the
$\omega\propto k^z$ dispersion relation with dynamical exponent $z=3/2$.
