Not yet reviewed by Pith; the record is open.

We compute the production rates for two, three, four and five jets in the hadronic decay of a Higgs boson in its two dominant decay modes to bottom quarks and gluons to third order in the QCD coupling constant. The five-, four- and three-jet rates are obtained from a next-to-next-to-leading order (NNLO) calculation of Higgs decay to three jets, while the two-jet rate is inferred at next-to-next-to-next-to-leading order (N$^3$LO) from the inclusive decay rate. Our results show distinct differences in the dependence of the jet rates on the jet resolution parameter between the two decay modes, supporting the aim of discriminating different Higgs boson decay channels via classic QCD observables.