We propose a simple (most economic, based on gravity and supersymmetry only) and viable realization of cosmological (chaotic) inflation of early Universe. It is based on a new theory of supergravity that we call F(R) supergravity. The F(R) supergravity can be understood as the N=1 locally supersymmetric extension of popular theories of f(R) gravity in four spacetime dimensions. Our proposal to inflation uses the supersymmetric extension of the (R+R^2) inflationary model of Starobinsky. The F(R) supergravity theory was invented by me just for that purpose. In my talk I review the Starobinsky inflation, the F(R) supergravity and their applications to the Early Universe cosmology. However, those are not the only features of the proposed approach. The universal reheating and particle production after inflation in the context of F(R) supergravity are briefly discussed too.