  Meson-exchange current (MEC) contributions to the parity-violating (PV)
asymmetry for elastic scattering of polarized electrons from $^4$He are
calculated over a range of momentum transfer using Monte Carlo methods and a
variational $^4$He ground state wavefunction. The results indicate that MEC's
generate a negligible contribution to the asymmetry at low-$|\qv|$, where a
determination of the nucleon's mean square strangeness radius could be carried
out at CEBAF. At larger values of momentum transfer -- beyond the first
diffraction minimum -- two-body corrections from the $\rho$-$\pi$ \lq\lq
strangeness charge" operator enter the asymmetry at a potentially observable
level, even in the limit of vanishing strange-quark matrix elements of the
nucleon. For purposes of constraining the nucleon's strangeness electric form
factor, theoretical uncertainties associated with these MEC contributions do
not appear to impose serious limitations.
