  The utility of prompt photon plus associated jet production for constraining
the size and shape of the polarized gluon density of the proton $\Delta G$ is
examined at $\sqrt{S}=40$ GeV, appropriate for the proposed HERA-$\vec{N}$
polarized $\vec{p}\vec{p}$ collider experiment. The calculation is performed at
next-to-leading order (O($\alpha\alpha_s^2$)) in QCD. The reliability of the
predictions are examined in some detail.
