The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré 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

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... 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.