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 preinflationary 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.