  Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a closed, Ahlfors-David regular
set of dimension $n$ satisfying the "Riesz Transform bound"
$$\sup_{\varepsilon>0}\int_E\left|\int_{\{y\in
E:|x-y|>\varepsilon\}}\frac{x-y}{|x-y|^{n+1}} f(y) dH^n(y)\right|^2 dH^n(x)
\leq C \int_E|f|^2 dH^n .$$ Assume further that $E$ is the boundary of a domain
$\Omega\subset \mathbb{R}^{n+1}$ satisfying the Harnack Chain condition plus an
interior (but not exterior) Corkscrew condition. Then $E$ is uniformly
rectifiable.
