Neutron capture by 127,129I has been measured using the Oak Ridge Electron Linear Accelerator as a pulsed neutron source. Neutron energies were determined by time-of-flight. Resonance peaks were parameterized for radioactive 129I up to 3400 eV and for stable 127I from 2660 to 4260 eV. Average capture cross sections were derived for 129I from 3 to 500 keV and for 129I from 3 to 2200 keV. Over the 3- to 100-keV range, the 129I cross sections average ∼70% of the corresponding 127I cross sections but show much more fluctuation as a function of energy. The greater fluctuation is attributed to the approximately three times wider level spacing.