  A cosmological constant in the regime of low space-time curvature is
calculated in the recently proposed version of F(R) supergravity with a generic
cubic function F. The F(R) supergravity is the N=1 supersymmetric extension of
f(R) gravity. The cubic model is known to successfully describe a chaotic
(slow-roll) inflation in the regime of high space-time curvature. We find that
a simple extension of the same model allows a positive cosmological constant in
the regime of low space-time curvature. The inflaton superfield in F(R)
supergravity (like inflaton in f(R) gravity) violates the Strong Energy
Condition and thus breaks the restriction of the standard supergravity (with
usual matter) that can only have either a negative or vanishing cosmological
constant.
