  We construct a family of chiral anomaly-free supergravity theories in D=6
starting from D=7 supergravity with a gauged noncompact R-symmetry, employing a
Horava-Witten bulk-plus-boundary construction. The gauged noncompact R-symmetry
yields a positive (de Sitter sign) D=6 scalar field potential. Classical
anomaly inflow which is needed to cancel boundary-field loop anomalies requires
careful consideration of the gravitational, gauge, mixed and local
supersymmetry anomalies. Coupling of boundary hypermultiplets requires care
with the Sp(1) gauge connection required to obtain quaternionic Kahler target
manifolds in D=6. This class of gauged R-symmetry models may be of use as
starting points for further compactifications to D=4 that take advantage of the
positive scalar potential, such as those proposed in the scenario of
supersymmetry in large extra dimensions.
