  We study Coleman-De Luccia tunneling of the Standard Model Higgs field during
inflation in the case when the electroweak vacuum is metastable. We verify that
the tunneling rate is exponentially suppressed. The main contribution to the
suppression is the same as in flat space-time. We analytically estimate the
corrections due to the expansion of the universe and an effective mass term in
the Higgs potential that can be present at inflation.
