The s-wave π-π scattering amplitude is calculated by using the chain approximation from the nonrenormalizable interaction Lagrangian which gives rise to the same p-wave scattering amplitude as obtained by Frazer and Fulco from the dispersion relation. It is found that the s-wave amplitude contains two additional parameters. This appearance of new parameters is inevitable since the interaction is nonrenormalizable. The connection of our method of solution with that of the dispersion relation is also discussed. Our calculation gives rise to a low energy resonance in the I=0 state which may be identified as the resonance observed by Booth et al.