We study gravitational particle production of the massive spin-3/2 Rarita-Schwinger field, and its close relative, the gravitino, in Friedmann-Robertson-Walker cosmological spacetimes. For masses lighter than the value of the Hubble expansion rate after inflation, m3/2≲H, we find catastrophic gravitational particle production, wherein the number of gravitationally produced particles is divergent, caused by a transient vanishing of the helicity-1/2 gravitino sound speed. In contrast with the conventional gravitino problem, the spectrum of produced particles is dominated by those with momentum at the UV cutoff. This suggests a breakdown of effective field theory, which might be cured by new degrees of freedom that emerge in the UV. We study the UV completion of the Rarita-Schwinger field, namely N=1, d=4, supergravity. We reproduce known results for models with a single superfield and models with an arbitrary number of chiral superfields, find a simple geometric expression for the sound speed in the latter case, and extend this to include nilpotent constrained superfields and orthogonal constrained superfields. We find supergravity models where the catastrophe is cured and models where it persists. Insofar as quantizing the gravitino is tantamount to quantizing gravity, as is the case in any UV completion of supergravity, the models exhibiting catastrophic production are prime examples of four-dimensional effective field theories that become inconsistent when gravity is quantized, suggesting a possible link to the swampland program. We propose the gravitino swampland conjecture, which is consistent with and indeed follows from the Kachru-Kallosh-Linde-Trivedi and large volume scenarios for moduli stabilization in string theory.