  We analyze the chiral separation effect (CSE) in QCD by using the
gauge/gravity duality. In QCD, this effect arises from a combination of chiral
anomalies and the axial $U(1)$ anomaly. Due to the axial gluon anomaly, the
value of the CSE conductivity is not determined by the anomalies of QCD but
receives radiative corrections, which leads to nontrivial dependence on
temperature and density. To analyze this dependence, we use different variants
of V-QCD, a complex holographic model, carefully fitted to QCD data. We find
our results for the anomalous CSE conductivity at small chemical potential and
nonzero temperature to be in good qualitative agreement with recent results
from lattice QCD simulations. We furthermore give predictions for the behavior
of the conductivity at finite (vectorial and axial) chemical potentials.
