  This paper is dedicated to the application of the DeGiorgi-Nash-Moser
regularity theory to the kinetic Fokker-Planck equation. This equation is
hypoelliptic. It is parabolic only in the velocity variable, while the
Liouville transport operator has a mixing effect in the position/velocity phase
space. The mixing effect is incorporated in the classical DeGiorgi method via
the averaging lemmas. The result can be seen as a H\"{o}lder regularity version
of the classical averaging lemmas.
