The cross section of the reaction 238U(n,γ)239U is measured at neutron energies of 23 and 964 keV. Photoneutron sources Sb-Be and Na-Be are calibrated using a manganese bath traceable to the National Bureau of Standards neutron source NBS-I and are provided nearly monoenergetic neutron irradiation. Neptunium-239 from the decay of 239U is chemically separated from the uranium target and is counted to determine the reaction rate. An 242Am foil is used as an absolute gamma-ray calibration standard in the determination of the induced activity. The resulting cross-section values are 491 ± 11 and 138 ± 5 mb at 23 and 967 keV, respectively.