  The chiral photocurrent or circular photogalvanic effect (CPGE) is a
photocurrent that depends on the sense of circular polarization. In a
disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the
effect is approximately quantized with a material-independent quantum $e^3/h^2$
for reasons of band topology. We study the first-order corrections due to the
Coulomb and Hubbard interactions in a continuum model of a Weyl semimetal in
which known corrections from other bands are absent. We find that the inclusion
of interactions generically breaks the quantization. The corrections are
similar but larger in magnitude than previously studied interaction corrections
to the (nontopological) linear optical conductivity of graphene, and have a
potentially observable frequency dependence. We conclude that, unlike the
quantum Hall effect in gapped phases or the chiral anomaly in field theories,
the quantization of the CPGE in Weyl semimetals is not protected but has
perturbative corrections in interaction strength.
