  We present viable F-term realizations of the hybrid inflationary scenario in
the context of supergravity addressing at the same time the well-known problems
of the initial conditions and of the adequate suppression of the inflaton mass.
An essential role in our construction is played by "decoupled" superheavy
fields without superpotential acquiring large vevs due to D-terms associated
with "anomalous" U(1) gauge symmetries. The naturalness of the initial
conditions is achieved through a "chaotic" inflation starting at energies close
to the Planck scale and driven by the "anomalous" D-terms. We discuss two
distinct mechanisms leading to such an early "chaotic" D-term inflation which
depend on the choice of the K\"ahler potential involving the superheavy fields.
The one relies on a choice of the K\"ahler potential of the $SU(1,1)/U(1)$
K\"ahler manifold of the type encountered in no-scale supergravity whereas the
other employs a more "conventional" choice for the K\"ahler potential of the
$SU(1,1)/U(1)$ or $SU(2)/U(1)$ K\"ahler manifold but invokes rather specific
valuesof the Fayet-Iliopoulos $\xi$ term.
