  We report the first measurement of the longitudinal double-spin asymmetry
$A_{LL}$ for mid-rapidity di-jet production in polarized $pp$ collisions at a
center-of-mass energy of $\sqrt{s} = 200$ GeV. The di-jet cross section was
measured and is shown to be consistent with next-to-leading order (NLO)
perturbative QCD predictions. $A_{LL}$ results are presented for two distinct
topologies, defined by the jet pseudorapidities, and are compared to
predictions from several recent NLO global analyses. The measured asymmetries,
the first such correlation measurements, support those analyses that find
positive gluon polarization at the level of roughly 0.2 over the region of
Bjorken-$x > 0.05$.
