The Argonne fast chopper has been used to measure the distribution of the sum of the intensities of transitions having energies between 3.8 and 4.2 MeV in the neutron-capture spectra of 12 neutron resonances of U238. The pulse-height spectra were observed in a large (8×6 in.) NaI(Tl) scintillator. The partial radiation widths exhibit large fluctuations. If the observed distribution is characterized by a number ν of degrees of freedom, as in the theoretical treatment by Porter and Thomas, a value of ν=5.8+/-2.3 is obtained. This is in contrast to the previously reported results which range from 11 to 90 and is consistent with the predictions of the simple statistical model for the distribution of the sum of four uncorrelated partial radiation widths.