  This paper investigates a background charge one Skyrme field chirally coupled
to light fermions on the 3-sphere. The Dirac equation for the system commutes
with a generalised angular momentum or grand spin. It can be solved explicitly
for a Skyrme configuration given by the hedgehog form. The energy spectrum and
degeneracies are derived for all values of the grand spin. Solutions for
non-zero grand spin are each characterised by a set of four polynomials. The
paper also discusses the energy of the Dirac sea using zeta function
regularization.
