  We study the behavior of two planes of Quantum Heisenberg Antiferromagnet in
the regime in which a Chiral Spin Liquid is stabilized in each plane. The
planes are coupled by an exchange interaction of strength $J_3$. We show that
in the regime of small $J_3$ (for both ferromagnetic {\it and}
antiferromagnetic coupling), the system dynamically selects an
\underline{antiferromagnetic} ordering of the ground state {\it chiralities} of
the planes. For the case of an antiferromagnetic interaction between the
planes, we find that, at some critical value $J_3^c$ of the inter-layer
coupling, there is a phase transition to a valence-bond state on the interlayer
links. We derive an effective Landau-Ginzburg theory for this phase transition.
It contains two $U(1)$ gauge fields coupled to the order parameter field. We
study the low energy spectrum of each phase. In the condensed phase an
``anti-Higgs-Anderson" mechanism occurs. It effectively restores time-reversal
invariance by rendering massless one of the gauge fields while the other field
locks the chiral degrees of freedom locally. There is no phase transition for
ferromagnetic couplings.
