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We show that the parity of the $h Z\gamma$ vertex can be probed byinterference between the gluon fusion Higgs production, $gg \to h \to \gamma Z\to \gamma \ell^+\ell^-$, and the background, $gg \to \gamma Z \to \gamma\ell^+\ell^-$, amplitudes. In the presence of a parity violating $hZ\gamma$vertex, this interference alters the kinematic distribution of the leptons andphoton compared to Standard Model (SM) expectations. For a Higgs with SM-sizedwidth and couplings, we find that the size of the effect enters at most at the$10^{-2}$ level. Such a small effect cannot be seen at the LHC, even withfuturistic high luminosities. Should there exist other broader scalar particleswith larger production cross-section times branching ratio to $Z\gamma$, thenthe parity structure of their $Z\gamma$ couplings can be probed with thistechnique.

Probing CP Violation in $h \to Z\gamma$ with Background Interference