We have measured for the first time the cross section of the 2 H(n, γ ) 3 H reaction at an energy relevant to big-bang nucleosynthesis by employing a prompt discrete γ -ray detection method. The outgoing photons have been detected by means of anti-Compton NaI(Tl) spectrometers with a large signal-to-noise ratio. The resulting cross sections are 2.23 ± 0.34, 1.99 ± 0.25, and 3.76 ± 0.41µb at E n = 30.5, 54.2, and 531 keV, respectively. At E n = 30.5 keV the cross section differs from the value reported previously by a factor of 2. Based on the present data the reaction rate has been obtained for temperatures in the range 10 7 − 10 10 K. The astrophysical impact of the present result is discussed. The obtained cross sections are compared with a theoretical calculation based on the Faddeev approach, which includes meson exchange currents as well as a three-nucleon force.