  We report the first measurement of the target single-spin asymmetry, $A_y$,
in quasi-elastic scattering from the inclusive reaction
$^3$He$^{\uparrow}(e,e^\prime)$ on a $^3$He gas target polarized normal to the
lepton scattering plane. Assuming time-reversal invariance, this asymmetry is
strictly zero for one-photon exchange. A non-zero $A_y$ can arise from the
interference between the one- and two-photon exchange processes which is
sensitive to the details of the sub-structure of the nucleon. An experiment
recently completed at Jefferson Lab yielded asymmetries with high statistical
precision at $Q^{2}=$ 0.13, 0.46 and 0.97 GeV$^{2}$. These measurements
demonstrate, for the first time, that the $^3$He asymmetry is clearly non-zero
and negative with a statistical significance of (8-10)$\sigma$. Using measured
proton-to-$^{3}$He cross-section ratios and the effective polarization
approximation, neutron asymmetries of $-$(1-3)% were obtained. The neutron
asymmetry at high $Q^2$ is related to moments of the Generalized Parton
Distributions (GPDs). Our measured neutron asymmetry at $Q^2=0.97$ GeV$^2$
agrees well with a prediction based on two-photon exchange using a GPD model
and thus provides a new, independent constraint on these distributions.
