  Chiral antisymmetric tensor fields can have chiral couplings to quarks and
leptons. Their kinetic terms do not mix different representations of the
Lorentz symmetry and a local mass term is forbidden by symmetry. The chiral
couplings to the fermions are asymptotically free, opening interesting
perspectives for a possible solution to the gauge hierarchy problem. We argue
that the interacting theory for such fields can be consistently quantized, in
contrast to the free theory which is plagued by unstable solutions. We suggest
that at the scale where the chiral couplings grow large the electroweak
symmetry is spontaneously broken and a mass term for the chiral tensors is
generated non-perturbatively. Massive chiral tensors correspond to massive spin
one particles that do not have problems of stability. We also propose an
equivalent formulation in terms of gauge fields.
