  We present the Higgs boson production cross section at Hadron colliders in
the gluon fusion production mode through N3LO in perturbative QCD.
Specifically, we work in an effective theory where the top quark is assumed to
be infinitely heavy and all other quarks are considered to be massless. Our
result is the first exact formula for a partonic hadron collider cross section
at N3LO in perturbative QCD. Furthermore, this result represents the first
analytic computation of a hadron collider cross section involving elliptic
integrals. We derive numerical predictions for the Higgs boson cross section at
the LHC. Previously this result was approximated by an expansion of the cross
section around the production threshold of the Higgs boson and we compare our
findings. Finally, we study the impact of our new result on the state of the
art prediction for the Higgs boson cross section at the LHC.
