For the first time, the recently predicted chemical shift of neutron resonances, to be regarded as an analogue to the Mössbauer isomer shift, has been experimentally observed studying the 6.67 eV resonance of 238U. The experimental shifts were determined by a chi-square fitting technique from the time-of-flight transmission spectra of metallic uranium and four uranium compounds measured at the Dubna IBR-30 pulsed reactor. A computational method has been applied to estimate, and compensate for, the influence of the crystal-lattice vibrations on the experimental values thus obtained. The electron density differences at the nucleus have been calculated for the various sample pairs using available data on chemical X-ray shifts in uranium compounds, on Mössbauer isomer shifts in isovalent neptunium compounds and on free-ion electron densities. The resonance shift results lead to the conclusion that the mean-square charge radius of 238U diminishes by 1.7 -0.8+1.2 fm 2 upon capturing the resonance neutron.