We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N3LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N3LO corrections are of the order of +2.2%. The total scale variation at N3LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.