Measured values of the differential cross sections for pion-nucleon charge exchange, pi- p --> pi0 n, are presented for pi- momenta of 103, 112, 120, 130, 139, 152, and 178 MeV/c. Complete angular distributions were obtained by using the Crystal Ball detector at the Alternating Gradient Synchrotron at Brookhaven National Laboratory. Statistical uncertainties of the differential cross sections vary from 3% to 6% in the backward angle region, and from 6% to about 20% in the forward region with the exception of the two most forward angles. The systematic uncertainties are estimated to be about 3% for all momenta.