Absolute 125-deg differential gamma-ray production cross sections have been measured for 21 gamma rays produced in natural chromium by the (n,n′γ) reaction in the incident neutron energy range from 0.84 to 3.97 MeV. The pulsed beam time-of-flight technique was employed for background reduction. The data were corrected for neutron multiple scattering and neutron and gamma-ray attenuations in the scattering sample. Angle-integrated gamma-ray production cross sections were inferred from the differential measurements using gamma-ray angular distributions obtained from compound nucleus statistical model calculations. On the basis of the angle-integrated cross sections and measured branching ratios, neutron inelastic scattering cross sections were deduced for 22 energy levels in the four naturally occurring isotopes of chromium. These results are compared to previous measurements and the Evaluated Nuclear Data File (ENDF/B-IV, MAT 1191). The present measurements suggest that in the threshold energy region for inelastic neutron scattering to each of the first excited 2+-states in 50,52,54Cr, the cross sections are significantly overestimated in ENDF/B-IV.