  A duality argument for the recently discovered chiral-nematic phase of the XY
model in a triangular lattice is presented. We show that a new Ising variable
naturally emerges in mapping the antiferromagnetic J1-J2 classical XY spin
Hamiltonian onto an appropriate Villain model on a triangular lattice. The new
variable is the chirality degree of freedom, which exists in addition to the
usual vortex variables, in the dual picture. Elementary excitations and the
associated phase transition of the Ising degrees of freedom are discussed in
some detail.
