  We estimate the equilibration rate of a nearly homogeneous Higgs field,
displaced from its ground state during the onset of an electroweak phase
transition. The computation is carried out with Hard Thermal Loop resummed
perturbation theory, and a significant part of the result originates from
Bose-enhanced $t$-channel $2\leftrightarrow 2$ scatterings. The expression is
shown to be IR finite and gauge independent. Possible applications to Langevin
simulations of bubble nucleation are mentioned, and we also contrast with the
friction affecting bubble growth.
