  We re-examine the theoretical uncertainty in the Standard Model expression
for $B^0$-$\bar{B}^0$ mixing. We focus on lattice calculations of the ratio
$\xi$, needed to relate the oscillation frequency of $B^0_s$-$\bar{B}^0_s$
mixing to the poorly known CKM element $V_{td}$. We replace the usual linear
chiral extrapolation with one that includes the logarithm that appears in
chiral perturbation theory. We find a significant shift in the ratio $\xi$,
from the conventional $1.15\pm0.05$ to $\xi=1.32\pm0.10$.
