  We calculate the target normal single-spin asymmetry caused by two-photon
exchange in inclusive electron-nucleon scattering in the resonance region. Our
analysis uses the $1/N_c$ expansion of low-energy QCD and combines $N$ and
$\Delta$ intermediate and final states using the contracted $SU(4)$ spin-flavor
symmetry. The normal spin asymmetry obtained in leading-order accuracy in
$1/N_c$ has magnitude $\sim 10^{-2}$ and different sign in $ep$ and $en$
scattering. It can be measured in electron scattering at lab energies $\sim$
0.5-1.5 GeV and provides a clean probe of two-photon exchange dynamics.
