We present a next-to-leading order QCD calculation for single-inclusive
high-p_T jet production in longitudinally polarized pp collisions within the
``small-cone'' approximation. The fully analytical expressions obtained for the
underlying partonic hard-scattering cross sections greatly facilitate the
analysis of upcoming BNL-RHIC data on the double-spin asymmetry A_{LL}^{jet}
for this process in terms of the unknown polarization of gluons in the nucleon.
We simultaneously rederive the corresponding QCD corrections to unpolarized
scattering and confirm the results existing in the literature. We also
numerically compare to results obtained with Monte-Carlo methods and assess the
range of validity of the ``small-cone'' approximation for the kinematics
relevant at BNL-RHIC.Comment: 23 pages, 8 eps-figure