The discovery of fading but relatively long-lived X-ray emission(1) accompanying gamma-ray bursts has revolutionized the study of these objects. This ＇afterglow＇ is most easily explained by models(2-4) similar to those describing supernovae, but with relativistic ejecta. And as with supernovae, afterglow measurements should in principle provide important constraints on burst properties, permitting, for example, estimates of the amount of energy released, the geometry of the emitting surface and the density of the ambient medium, Here we report infrared observations of the fading optical transient(5) associated with the burst of 14 December 1997 (GRB971214;ref. 6). We detect a ＇break＇ in the broad-band spectrum, as predicted by afterglow models, which constrains the total energy in the burst to be > 10(51) erg. Combining the fluence of optical afterglow with the redshift (z = 3.42; ref. 7), we estimate that the energy released in the afterglow alone was 2 x 10(51) erg. Estimates of afterglow energetics are less likely to be subject to geometric effects-such as beaming-that render uncertain estimates of the total burst energy, but it nevertheless appears from our measurements that gamma-ray bursts may be much more energetic than the 10(51) erg usually assumed.