  We consider the effect of a period of inflation with a high energy density
upon the stability of the Higgs potential in the early universe. The recent
measurement of a large tensor-to-scalar ratio, $r_T \sim 0.16$, by the BICEP-2
experiment possibly implies that the energy density during inflation was very
high, comparable with the GUT scale. Given that the standard model Higgs
potential is known to develop an instability at $\Lambda \sim 10^{10}$ GeV this
means that the resulting large quantum fluctuations of the Higgs field could
destabilize the vacuum during inflation, even if the Higgs field starts at zero
expectation value. We estimate the probability of such a catastrophic
destabilisation given such an inflationary scenario and calculate that for a
Higgs mass of $m_h=125.5$ GeV that the top mass must be less than $m_t\sim 172$
GeV. We present two possible cures: a direct coupling between the Higgs and the
inflaton and a non-zero temperature from dissipation during inflation.
