  We discuss, in the context of $N=1$ hidden sector non-minimal supergravity
chaotic inflationary models, constraints on the parameters of a polynomial
superpotential resulting from existing bounds on the reheating temperature and
on the amplitude of the primordial energy density fluctuations as inferred from
COBE. We present a specific two-parameter chaotic inflationary model which
satisfies these constraints and discuss a possible scenario for adequate baryon
asymmetry generation.
