  The vector analyzing power A_n is calculated for elastic electron scattering
from a variety of spin zero nuclei at energies from 14 MeV to 3 GeV. Time
reversal symmetry insures that A_n vanish in first Born approximation.
Therefore A_n depends on Coulomb distortions and can be large for scattering
from heavy nuclei. The vector analyzing power is a potential source of
systematic error for parity violation experiments. We find that A_n=-0.361 ppm
for the kinematics of the Parity Radius Experiment (PREX) involving 850 MeV
electrons scattering at six degrees from 208Pb. This is comparable to the
parity violating asymmetry. However for HAPPEX He involving 3 GeV electrons
scattering on 4He we find that A_n is very small.
