  We propose a class of models in which the $\eta$-problem of supersymmetric
hybrid inflation is resolved using a Heisenberg symmetry, where the associated
modulus field is stabilized and made heavy with the help of the large vacuum
energy during inflation without any fine-tuning. The proposed class of models
is well motivated both from string theory considerations, since it includes the
commonly encountered case of no-scale supergravity Kaehler potential, and from
the perspective of particle physics since a natural candidate for the inflaton
in this class of models is the right-handed sneutrino which is massless during
the inflationary epoch, and subsequently acquires a large mass at the end of
inflation. We study a specific example motivated by sneutrino hybrid inflation
with no-scale supergravity in some detail, and show that the spectral index may
lie within the latest WMAP range, while the tensor-to-scalar ratio is very
small.
