The production of a single pion in pion-nucleon collisions has been studied by using the Chew-Low formalism with $p$-wave coupling. The equation for the $T$-matrix is solved by using the one-meson approximation. The solution is used to compute the cross sections for pion production and the two-meson corrections to the scattering equation of Chew and Low. The production cross sections show a peak due to overlapping final-state resonances, but have a magnitude of less than 2 mb, compared to the observed inelastic cross sections of about 20 mb (near 1 Bev). The two-meson corrections to scattering are found to be quite small.