  We prove that there are only finitely many distinct semi-simple gauge groups
and matter representations possible in consistent 6D chiral (1,0) supergravity
theories with one tensor multiplet. The proof relies only on features of the
low-energy theory; the consistency conditions we impose are that anomalies
should be cancelled by the Green-Schwarz mechanism, and that the kinetic terms
for all fields should be positive in some region of moduli space. This result
does not apply to the case of the non-chiral (1,1) supergravities, which are
not constrained by anomaly cancellation.
