  We have analyzed the single $\eegg + \slashchar{E}_T$ event at CDF and found
that the expected rate and kinematics are consistent with selectron pair
production. We consider two classes of general low-energy supersymmetric
theories, where either the lightest neutralino (``neutralino LSP'' scenario) or
the gravitino (``light gravitino'' scenario) is the lightest supersymmetric
particle. The parameter space of the supersymmetric Lagrangian is tightly
constrained by the kinematics of the event and the branching ratios for the
necessary decay chain of the selectron. We identify a region of the parameter
space satisfying all low-energy constraints, and consistent with the selectron
interpretation of the $ee\gamma\gamma + \Et$ event. We discuss other
supersymmetric processes at Fermilab Tevatron and at CERN LEP in both scenarios
that could confirm or exclude a supersymmetric explanation of the event, and
that could distinguish between the neutralino LSP and the light gravitino
scenarios.
