  Let $M$ be a closed hypersurface in a simply connected rank-1 symmetric space
$\olm$. In this paper, we give an upper bound for the first eigenvalue of the
Laplacian of $M$ in terms of the Ricci curvature of $\olm$ and the square of
the length of the second fundamental form of the geodesic spheres with center
at the center-of-mass of $M$.
