  We show that the standard model Higgs field can realize the quadratic chaotic
inflation, if the kinetic term is significantly modified at large field values.
This is a simple realization of the so-called running kinetic inflation. The
point is that the Higgs field respects an approximate shift symmetry at high
energy scale. The tensor-to-scalar ratio is predicted to be $r \simeq 0.13 -
0.16$, which nicely explains the primordial B-mode polarization,
$r=0.20^{+0.07}_{-0.05}$, recently discovered by the BICEP2 experiment. In
particular, allowing small modulations induced by the shift symmetry breaking,
the negative running spectral index can also be induced. The reheating
temperature is expected to be so high that successful thermal leptogenesis is
possible. The suppressed quartic coupling of the Higgs field at high energy
scales may be related to the Higgs chaotic inflation.
