We present a calculation of the Higgs boson decay into a quarkonium plus a
photon and show that the branching ratio is sensitive to both the magnitude and
sign of the Higgs-heavy quark coupling.
Our numerical results include relativistic corrections, as well as logarithms
of the Higgs mass divided by the heavy quark mass resummed to all orders in
$\alpha_s$, which is carried out in the next-to-leading logarithmic accuracy.
The resulting branching ratio shows that the Higgs-charm coupling should be
measurable at the high-luminosity LHC.