We present in these proceedings, our analysis (arXiv:2004.14398) 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 $\gamma_5$ 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 ones, 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.