  We present the first Bayesian inference of neutron star crust properties to
incorporate neutron skin data, including the recent PREX measurement of the
neutron skin of $^{208}$Pb, combined with recent chiral effective field theory
predictions of pure neutron matter with statistical errors. Using a
compressible liquid drop model with an extended Skyrme energy-density
functional, we obtain the most stringent constraints to date on the transition
pressure $P_{\rm cc}=0.33^{+0.07}_{-0.07}$ MeV fm$^{-3}$ and chemical potential
$\mu_{\rm cc}=12.6^{+1.8}_{-1.9}$ MeV (which control the mass, moment of
inertia and thickness of a neutron star crust), the proton fractions that
bracket the pasta phases $y_{\rm p}=0.115^{+0.016}_{-0.017}$ and $y_{\rm
cc}=0.041^{+0.007}_{-0.006}$, as well as the relative mass and moment of
inertia $\Delta M_{\rm p} / \Delta M_{\rm c}\approx \Delta I_{\rm p} / \Delta
I_{\rm c} = 0.54^{+0.05}_{-0.09}$ and thickness $\Delta R_{\rm p} / \Delta
R_{\rm c}=0.129^{+0.019}_{-0.030}$ of the layers of non-spherical nuclei
(nuclear pasta) in the crust.
