  We give the asymptotic behavior of the zeros of orthogonal polynomials, after
appropriate scaling, for which the orthogonality measure is supported on the
$q$-lattice $\{q^k, k=0,1,2,3,\ldots\}$, where $0 < q < 1$. The asymptotic
distribution of the zeros is given by the radial part of the equilibrium
measure of an extremal problem in logarithmic potential theory for circular
symmetric measures with a constraint imposed by the $q$-lattice.
