  We study a model of three $S=1/2$ antiferromagnetic Heisenberg spin chains
weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is
shown that the model exhibits a critical phase with central charge C=2 and
belongs to the class of ``chirally stabilized'' liquids recently introduced by
Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space,
we find an exact solution at a Toulouse point which captures all universal
properties of the model, including the SU(2) symmetric case. At the new
critical point the massless degrees of freedom are described in terms of an
effective $S = 1/2$ Heisenberg spin chain and two critical Ising models. We
discuss the spectral properties of the model, compute spin-spin correlation
functions and estimate the NMR relaxation rate.
