  In this paper we discuss decays of the Higgs boson to quarkonia in
association with a photon. We identify a new mechanism for producing such final
states in Higgs decays that leads to predictions for the decay rates that
differ by an order of magnitude from previous estimates. Although the branching
ratios for these processes are still small, the processes are experimentally
clean, and the H \to J/\psi+gamma decay should be observable at a 14 TeV LHC.
We point out that quantum interference between two different production
mechanisms makes the decay rates sensitive to the HQQbar couplings.
Consequently, measurements of the H \to J/\psi+gamma decay rate would allow one
to probe the Higgs-charm coupling directly at the LHC. We discuss the
experimental prospects for the observation of these decays and for the direct
measurement of the Hccbar coupling.
