A model of chaotic inflation based on the theory of a scalar field with potential \lambda \phi ^ { 4 } perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity - { \xi \over 2 } \phi ^ { 2 } R with \xi \gtrsim 0.002 . We describe embedding of this model into the superconformal theory with spontaneous breaking of superconformal symmetry , and into supergravity . A model with small \xi is technically natural : setting the small parameter \xi to zero leads to a point of enhanced symmetry in the underlying superconformal theory .