  In supergravity models with low supersymmetry breaking scale the gravitinos
can be superlight with mass in the micro-eV to keV range. In such a case,
gravitino emission provides a new cooling mechanism for protoneutron stars and
therefore can provide constraints on the mass of the superlight gravitino. This
happens because the coupling to matter of superlight gravitinos is dominated by
its goldstino component, whose coupling to matter is inversely proportional to
the scale of supersymmetry breaking and increases as the gravitino mass
decreases. Present observations therefore provide lower limits on the gravitino
mass. Using recently revised goldstino couplings, we find that the two dominant
processes in supernova cooling are $e^+e^-\to \tilde{G}\tilde{G}$ and
$\gamma+e^-\to e^-\tilde{G}\tilde{G}$. They lead to lower limits on the
supersymmetry breaking scale $\Lambda_{S}$ from 160 to 500 GeV for core
temperatures 30 to 60 MeV and electron chemical potentials 200 to 300 MeV. The
corresponding lower limits on the gravitino mass are $.6 - 6\times 10^{-6}$ eV.
