  We present detections of absorption from the ground state and excited states
of C I in the z = 1.9731 damped Ly\al\ system of the QSO 0013$-$004. The
excitation temperature between the J = 0 and J = 1 fine-structure levels of C I
is 11.6 $\pm$ 1.0 K. We estimate other contributions to the excitation of the C
I fine-structure levels, and use the population ratio of the excited state to
the ground state to derive an estimate for the cosmic microwave background
radiation (CMBR) temperature of T = 7.9 $\pm$ 1.0 K at 0.61 mm and z = 1.9731,
which is consistent with the predicted value of T = 8.105 $\pm$ 0.030 K from
the standard cosmology.
