  It is well known that large Hubble-induced supergravity corrections to the
inflaton field can ruin the flatness of the potential, thus creating a tension
between slow-roll inflation and supergravity. In this paper we show that it is
possible to obtain a {\it cosmologically flat} direction, embedded within the
minimal supersymmetric standard model, despite very large super-Hubble
corrections. As an illustration, we show that a flat direction which is lifted
by an $n=6$ operator matches the current cosmic microwave background data for a
wide range of the Hubble parameter, $10^{5} {\rm GeV}\lesssim H_{inf}\lesssim
10^{8.5}$ GeV. Our approach can be applied to any $F$-term inflationary model.
