  We investigate the recently proposed class of chaotic inflation models in
supergravity with an arbitrary inflaton potential. These models are extended to
include matter fields in the visible sector and we employ a mechanism of SUSY
breaking based on a particular phenomenological version of the KKLT mechanism
(the KL model). We describe specific features of reheating in this class of
models and show how one can solve the cosmological moduli and gravitino
problems in this context.
