We study a recently proposed running kinetic inflation model in which the inflaton potential becomes flat due to rapid growth of the kinetic term at large inflaton field values. As concrete examples, we build a variety of chaotic inflation models in supergravity with e.g. quadratic, linear, and fractional-power potentials. The power of the potential generically increases after inflation, and the inflaton is often massless at the potential minimum in the supersymmetric limit, which leads to many interesting phenomena. First, the light inflaton mass greatly relaxes severe thermal and non-thermal gravitino problems. Secondly, the kination epoch is naturally present after inflation, which may enhance the gravity waves. Thirdly, since the inflaton is light, it is likely coupled to the Higgs sector for successful reheating. The inflaton and its superpartner, inflatino, may be produced at the LHC. Interestingly, the inflatino can be dark matter, if it is the lightest supersymmetric particle.