  We prove a boundary Harnack inequality for nonlocal elliptic operators $L$ in
non-divergence form with bounded measurable coefficients. Namely, our main
result establishes that if $Lu_1=Lu_2=0$ in $\Omega\cap B_1$, $u_1=u_2=0$ in
$B_1\setminus\Omega$, and $u_1,u_2\geq0$ in $\mathbb R^n$, then $u_1$ and $u_2$
are comparable in $B_{1/2}$. The result applies to arbitrary open sets
$\Omega$.
  When $\Omega$ is Lipschitz, we show that the quotient $u_1/u_2$ is H\"older
continuous up to the boundary in $B_{1/2}$.
