  We establish a connection between the absolute continuity of elliptic measure
associated to a second order divergence form operator with bounded measurable
coefficients with the solvability of an endpoint $BMO$ Dirichlet problem. We
show that these two notions are equivalent. As a consequence we obtain an
end-point perturbation result, i.e., the solvability of the $BMO$ Dirichlet
problem implies $L^p$ solvability for all $p>p_0$.
