  We consider the production of gravitinos ($\widetilde G$) in association with
gluinos ($\tilde g$) or squarks ($\tilde q$) at hadron colliders, including the
three main sub-processes: $q \bar q -> \tilde g\widetilde G$, $qg -> \tilde
q\widetilde G$, and $gg -> \tilde g\widetilde G$. These channels become
enhanced to the point of being observable for sufficiently light gravitino
masses ($m_{\widetilde G} < 10^{-4} eV$), as motivated by some supersymmetric
explanations of the CDF $ee\gamma\gamma+ E_{T,miss}$ event. The characteristic
signal of such events would be monojets, as opposed to dijets obtained in the
more traditional supersymmetric process $p \bar p -> \tilde g\tilde g$.
Searches for such events at the Tevatron can impose lower limits on the
gravitino mass. In the Appendix, we provide a complete set of Feynman rules for
gravitino interactions used in our calculation.
