The resonant-neutron-capture γ-ray spectra for 28 resonances below 600-eV neutron energy are measured in U238(n,γ)U239 with improved neutron and γ-ray energy resolution to allow an accurate test of the predictions of the statistical model of neutron capture. No convincing departures from these predictions are observed. The variation over 23 S-wave neutron resonances of the γ-ray transition probabilities to 15 final states is consistent with the Porter-Thomas distribution for both E1 and M1 multipoles. There is also no statistically significant correlation between the different decay modes of the neutron resonances. A large correlation coefficient of + 0.81 is observed between the partial radiative widths of the 3991- and 3982- keV γ rays. This result, however, is not in violation of statistical independence for a sample size of 15 γ rays. The E1 and M1 γ-ray strength functions are (2.6 ± 0.4) × 10−3 and (8.1 ± 1.6) × 10−3, respectively, compared to 3 × 10−3 and 4 × 10−3 listed by Bartholomew as the median values of all nuclei. Three of the weaker resonances at 10.2, 89.5, and 263 eV are assigned to P-wave capture. The neutron binding energy is measured to be 4806.7 ± 2.0 keV, which is 5.0 keV higher than the previously accepted value. Previously unobserved γ-ray transitions are reported.