  We present precise predictions for the Higgs boson rapidity distribution at
the LHC in the gluon fusion production mode. Our approach relies on the fully
analytic computation of six terms in a systematic expansion of the partonic
differential cross section around the production threshold of the Higgs boson
at next-to-next-to-next-to leading order (N$^3$LO) in QCD perturbation theory.
We observe a mild correction compared to the previous perturbative order and a
significant reduction of the dependence of the cross section on the
perturbative scale throughout the entire rapidity range.
