  The problem of constructing consistent parity-violating interactions for
spin-3 gauge fields is considered in Minkowski space. Under the assumptions of
locality, Poincar\'e invariance and parity non-invariance, we classify all the
nontrivial perturbative deformations of the abelian gauge algebra. In
space-time dimensions $n=3$ and $n=5$, deformations of the free theory are
obtained which make the gauge algebra non-abelian and give rise to nontrivial
cubic vertices in the Lagrangian, at first order in the deformation parameter
$g$. At second order in $g$, consistency conditions are obtained which the
five-dimensional vertex obeys, but which rule out the $n=3$ candidate.
Moreover, in the five-dimensional first order deformation case, the gauge
transformations are modified by a new term which involves the second de
Wit--Freedman connection in a simple and suggestive way.
