  We examine the intrinsic spin-dependence of the dominant $gg \rightarrow
gggg$ subprocess contribution to four-jet production in polarized proton-proton
collisions using helicity amplitude techniques. We find that the partonic
level, longitudinal spin-spin asymmetry, $\hat{a}_{LL}$, is intrinsically large
in the kinematic regions probed in experiments detecting four isolated jets.
Such events may provide another qualitative or semi-quantitative test of the
spin-structure of QCD in planned polarized $pp$ collisions at RHIC.
