  We derive constraints on the time variation of the Higgs vacuum expectation
value $<\phi>$ through the effects on Big Bang nucleosynthesis (BBN) and the
cosmic microwave background (CMB). In the former case, we include the
(previously-neglected) effect of the change in the deuteron binding energy,
which alters both the $^4$He and deuterium abundances significantly. We find
that the current BBN limits on the relative change in \higgs are $-(0.6 - 0.7)
\times 10^{-2} < Delta<\phi>/<\phi> < (1.5 - 2.0) \times 10^{-2}$, where the
exact limits depend on the model we choose for the dependence of the deuteron
binding energy on \higgs.The limits from the current CMB data are much weaker.
