  We determine the limit distribution (as $\lambda \to \infty$) of complex
zeros for holomorphic continuations $\phi_{\lambda}^{\C}$ to Grauert tubes of
real eigenfunctions of the Laplacian on a real analytic compact Riemannian
manifold $(M, g)$ with ergodic geodesic flow. If $\{\phi_{j_k} \}$ is an
ergodic sequence of eigenfunctions, we prove the weak limit formula
$\frac{1}{\lambda_j} [Z_{\phi_{j_k}^{\C}}] \to \frac{i}{\pi} \bar{\partial}
{\partial} |\xi|_g$, where $ [Z_{\phi_{j_k}^{\C}}]$ is the current of
integration over the complex zeros and where $\bar{\partial}$ is with respect
to the adapted complex structure of Lempert-Sz\"oke and Guillemin-Stenzel.
