  We consider the supercritical elliptic problem -\Delta u = \lambda e^u,
\lambda > 0, in an exterior domain $\Omega = \mathbb{R}^N \setminus D$ under
zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N
greater or equal than 3. We prove that, for \lambda small, this problem admits
infinitely many regular solutions.
