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In this paper we discuss decays of the Higgs boson to quarkonia inassociation with a photon. We identify a new mechanism for producing such finalstates in Higgs decays that leads to predictions for the decay rates thatdiffer by an order of magnitude from previous estimates. Although the branchingratios for these processes are still small, the processes are experimentallyclean, 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 productionmechanisms makes the decay rates sensitive to the HQQbar couplings.Consequently, measurements of the H \to J/\psi+gamma decay rate would allow oneto probe the Higgs-charm coupling directly at the LHC. We discuss theexperimental prospects for the observation of these decays and for the directmeasurement of the Hccbar coupling.

Higgs boson decays to quarkonia and the Hccbar coupling