  Taken individually, magnetic monopoles and axions are both well-motivated
aspects of physics beyond the Standard Model. We demonstrate that by virtue of
the Witten effect, their interplay is furthermore nontrivial; monopoles break
the corresponding axial symmetries explicitly and result in an axion potential
lacking the usual instanton-derived exponential suppression factor. As axions
are distinguished by their extremely weak interactions, any regime where their
effects are enhanced may be of interest. As an application of these findings,
we demonstrate that a phenomenologically acceptable population of
grand-unification monopoles in the early Universe can efficiently suppress both
the QCD axion dark matter abundance and CMB isocurvature contribution.
