We report on the first 2-loop application of the BMHV scheme of dimensional regularisation with
non-anticommuting $\gamma_5$ to a non-abelian chiral
gauge theory. Two approaches to determine the breaking of the
Slavnov-Taylor identity on the regularised level are explained and
issues specific to the 2-loop level and to the non-abelian nature of
the theory are illustrated. The required 2-loop counterterm Lagrangian
that restores the validity of the Slavnov-Taylor identity is presented
and discussed. It contains a finite number of non-evanescent, UV
finite operators that contribute to all Green functions with physical
fields as well as to several Green functions corresponding to loop-corrected
BRST variations.