  We present the first precision measurement of the spin-dependent asymmetry in
the threshold region of $^3\vec{\rm He}(\vec{e},e')$ at $Q^2$-values of 0.1 and
0.2 (GeV/c)$^2$. The agreement between the data and non-relativistic Faddeev
calculations which include both final-state interactions (FSI) and
meson-exchange currents (MEC) effects is very good at $Q^2$ = 0.1 (GeV/c)$^2$,
while a small discrepancy at $Q^2$ = 0.2 (GeV/c)$^2$ is observed.
