The discovery of fading but relatively long-lived X-ray emission(1) ac
companying gamma-ray bursts has revolutionized the study of these obje
cts. This 'afterglow' is most easily explained by models(2-4) similar
to those describing supernovae, but with relativistic ejecta. And as w
ith supernovae, afterglow measurements should in principle provide imp
ortant constraints on burst properties, permitting, for example, estim
ates of the amount of energy released, the geometry of the emitting su
rface and the density of the ambient medium, Here we report infrared o
bservations of the fading optical transient(5) associated with the bur
st of 14 December 1997 (GRB971214;ref. 6). We detect a 'break' in the
broad-band spectrum, as predicted by afterglow models, which constrain
s the total energy in the burst to be > 10(51) erg. Combining the flue
nce of optical afterglow with the redshift (z = 3.42; ref. 7), we esti
mate that the energy released in the afterglow alone was 2 x 10(51) er
g. Estimates of afterglow energetics are less likely to be subject to
geometric effects-such as beaming-that render uncertain estimates of t
he total burst energy, but it nevertheless appears from our measuremen
ts that gamma-ray bursts may be much more energetic than the 10(51) er
g usually assumed.