  We study the Schr\"odinger operator $-\Delta -\alpha \delta (x-\Gamma)$ in
$L^2(\R^3)$ with a $\delta$ interaction supported by an infinite non-planar
surface $\Gamma$ which is smooth, admits a global normal parameterization with
a uniformly elliptic metric. We show that if $\Gamma $ is asymptotically planar
in a suitable sense and $\alpha>0$ is sufficiently large this operator has a
non-empty discrete spectrum and derive an asymptotic expansion of the
eigenvalues in terms of a ``two-dimensional'' comparison operator determined by
the geometry of the surface $\Gamma$. [A revised version, to appear in J. Phys.
A]
