  We show that if $\Omega$ is a vanishing chord-arc domain and $L$ is a
divergence-form elliptic operator with H\"older-continuous coefficient matrix,
then $\log k_L \in VMO$, where $k_L$ is the elliptic kernel for $L$ in the
domain $\Omega$. This extends the previous work of Kenig and Toro in the case
of the Laplacian.
