  Using elementary BRS cohomology theory, this paper describes a supergravity
anomaly analogous to, but very different from, the well known gauge and
gravitational anomalies. It closely resembles the known gauge anomalies, but it
results from a triangle diagram with two gravitinos and a gauge vector boson,
rather than three gauge vector bosons, or two gravitons and a vector boson. A
model that is likely to generate this supergravity anomaly is described. The
coefficient of this anomaly, in perturbation theory, in a theory with unbroken
supersymmetry, appears to be zero, because no relevant diagrams are linearly
divergent. However, when, and only when, the theory has spontaneously broken
supergravity, there are counterterms in the action which contribute to linearly
divergent diagrams that can generate the anomaly. From the relevant Feynman
diagrams in the theory, the general form of the anomaly can be conjectured. It
is proportional to the VEV $\left< D^a \right>$ of the auxiliary field for the
vector boson. So removing the anomaly generates a requirement that the
effective spontaneous breaking of supergravity needs to be of the purely chiral
type with $\left< F^i \right> \not = 0$ and with $\left< D^a \right>=0$.
