  We investigate a nonsingular initial state of the Universe which leads to
inflation naturally. The model is described by a scalar field with a quadratic
potential in Eddington-inspired Born-Infeld gravity. The curvature of this
initial state is given by the mass scale of the scalar field which is much
smaller than the Planck scale. Therefore, in this model, quantum gravity is not
necessary in understanding this pre-inflationary stage, no matter how large the
energy density becomes. The initial state in this model evolves eventually to a
long inflationary period which is similar to the usual chaotic inflation.
