  We analyze the asymptotic distribution of roots of Charlier polynomials with
negative parameter depending linearly on the index. The roots cluster on curves
in the complex plane. We determine implicit equations for these curves and
deduce the limiting density of the root distribution supported on these curves.
The proof is based on a determination of the limiting Cauchy transform in a
specific region and a careful application of the saddle point method. The
obtained result represents a solvable example of a more general open problem.

Classical Analysis and ODEs