  We consider the translationally invariant but parity (left-right symmetry)
breaking Ising chain Hamiltonian \begin{equation} {\cal H} = -U_2\sum_{k}
s_{k}s_{k+1} - U_3\sum_{k} s_{k}s_{k+1}s_{k+3} \nonumber \end{equation} and let
this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations
show that perturbations forcing this system off equilibrium make it act as a
Brownian molecular motor which, in the lattice gas interpretation, transports
particles along the chain. We determine the particle current under various
different circumstances, in particular as a function of the ratio $U_3/U_2$ and
of the conserved magnetization $M=\sum_k s_k$. The symmetry of the $U_3$ term
in the Hamiltonian is discussed

Statistical Mechanics