HOT Big Bang cosmology predicts that the temperature of the cosmic mic
rowave background radiation will increase linearly with increasing red
shift to early in the history of the Universe. The local background te
mperature (2.7 K) is known very accurately from direct measurements(1-
3), but other techniques must be used to estimate it at non-zero redsh
ifts. One way is to determine the excitation of atomic transitions in
absorbing clouds along the lines-of-sight to distant quasars(4). When
the transitions are in equilibrium with the microwave background radia
tion, the radiation will populate the fine-structure levels of the gro
und states of certain atoms, and the relative populations of the level
s can be used to calculate its temperature. Here we report the detecti
on of absorption from the first fine-structure level of neutral carbon
atoms in a cloud at a redshift of 1.776, towards the quasar Q1331 + 1
70. The population ratio yields a temperature of 7.4 +/- 0.8 K, assumi
ng that no other significant sources of excitation are present. This a
grees with the theoretical prediction of 7.58 K.