  Parity violating electron nucleus scattering is a clean and powerful tool for
measuring the spatial distributions of neutrons in nuclei with unprecedented
accuracy. Parity violation arises from the interference of electromagnetic and
weak neutral amplitudes, and the $Z^0$ of the Standard Model couples primarily
to neutrons at low $Q^2$. Experiments are now feasible at existing facilities.
We show that theoretical corrections are either small or well understood, which
makes the interpretation clean. A neutron density measurement may have many
implications for nuclear structure, atomic parity nonconservation experiments,
and the structure of neutron stars.
