  We study the dispersionless version of the recently introduced constrained
Toda hierarchy. Like the Toda lattice itself, it admits three equivalent
formulations: the formulation in terms of Lax equations, the formulation of the
Zakharov-Shabat type and the formulation through the generating equation for
the dispersionless limit of logarithm of the tau-function. We show that the
dispersionless constrained Toda hierarchy describes conformal maps of
reflection-symmetric planar domains to the exterior of the unit disc. We also
find finite-dimensional reductions of the hierarchy and show that they are
characterized by a differential equation of the L\"owner type which we call the
symmetric radial L\"owner equation. It is also shown that solutions to the
symmetric radial L\"owner equation are conformal maps of the exterior of the
unit circle with two symmetric slits to the exterior of the unit circle.
