c=1 String as the Topological Theory of the Conifold

We show that the non-critical $c=1$ string at the self-dual radius is equivalent to topological strings based on the deformation of the conifold singularity of Calabi-Yau threefolds. The Penner sum giving the genus expansion of the free energy of the $c=1$ string theory at the self-dual radius therefore gives the universal behaviour of the topological partition function of a Calabi-Yau threefold near a conifold point.