  We consider a chain described by a next-nearest-neighbor hopping combined
with a nearest-neighbor spin flip. In two dimensions this three-body term
arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a
generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond
superconductivity of predominantly $d$-wave symmetry. Solving the ground state
and low-energy excitations by analytical and numerical methods we find that the
chain is a Luther-Emery liquid with correlation exponent $K_{\rho} =
(2-n)^2/2$, where $n$ is the particle density.
