  Recently there has been a lot of interest in models in which gravity becomes
strong at the TeV scale. The observed weakness of gravitational interactions is
then explained by the existence of extra compact dimensions of space, which are
accessible to gravity but not to Standard Model particles. In this letter we
consider graviton emission into these extra dimensions from a hot supernova
core. The phenomenology of SN1987A places strong constraints on this energy
loss mechanism, allowing us to derive a bound on the fundamental Planck scale.
For the case of two extra dimensions we obtain a very strong bound of M > 50
TeV, which corresponds to a radius R < 0.3 microns. While there are a lot of
sources of uncertainty associated with this bound, we find that pushing it down
to the few-TeV range, which could in principle be probed by ground-based
experiments, is disfavored. For three or more extra dimensions the SN1987A
constraints do not exclude a TeV gravitational scale.
