  We prove the existence of a homogenization limit for solutions of
appropriately formulated sequences of boundary obstacle problems for the
Laplacian on $C^{1,\alpha}$ domains. Specifically, we prove that the energy
minimizers $u_\epsilon$ of $\int |\nabla u_\epsilon|^2 dx$, subject to $u \geq
\phi$ on a subset $S_\epsilon$, converges weakly in $H^1$ to a limit $\bar{u}$
which minimizes the energy $\int |\nabla \bar{u}|^2 dx + \int_\Sigma
(u-\phi)_-^2 \mu(x) dS_x$, $\Sigma \subset \partial D$, if the obstacle set
$S_\epsilon$ shrinks in an appropriate way with the scaling parameter
$\epsilon$. This is an extension of a result by Caffarelli and Mellet, which in
turn was an extension of a result of Cioranescu and Murat.
