  We study relationships between the neutron-rich skin of a heavy nucleus and
the properties of neutron-star crusts. Relativistic effective field theories
with a thicker neutron skin in $^{208}$Pb have a larger electron fraction and a
lower liquid-to-solid transition density for neutron-rich matter. These
properties are determined by the density dependence of the symmetry energy
which we vary by adding nonlinear couplings between isoscalar and isovector
mesons. An accurate measurement of the neutron radius in $^{208}$Pb---via
parity violating electron scattering---may have important implications for the
structure of neutron stars.
