We present in these proceedings, our analysis [1] at one-loop level within the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme of Dimensional Regularization, of the counterterm structure arising due to the presence of the γ 5 matrix and the breaking of the BRST invariance, in a massless chiral Yang-Mills theory supplemented with real scalars. The full one-loop counterterm structure necessary for the renormalization is obtained. This comprises the singular counterterms, including evanescent

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... nes, and by using techniques from algebraic renormalization the symmetry-restoring finite counterterms are evaluated as well. The latter are required to restore the BRST invariance, central to the consistency of the theory and for higher-order calculations. The renormalization group equations are derived within this framework, and are compared with the more "familiar" calculation in the context of symmetry-invariant renormalization.