  We give a brief sketch of lattice structure function calculations and review
previous results for the axial coupling $g_A$. We outline a new technique for
treating fermions on the lattice that preserves chiral symmetry, domain wall
fermions. Finally, we give preliminary results for the nucleon spectrum using
this new technique. Remarkably, a large mass splitting between the $N$ and
$N^*$, roughly consistent with experiment, is produced in the calculation.
These results are encouraging for proposed calculations of nucleon structure
functions.
