We present the first direct evidence for cold gas in a high redshift DLA galaxy. We measured several multiplets of weak neutral carbon (CI) transitions in order to perform a curve of growth analysis. A delta chi-squared test constrains the best fit Doppler parameter, b = 0.33_{-0.04}^{+0.05} km/s, and logN(CI) = 13.30 +- 0.2 cm^-2. This Doppler parameter constrains the kinetic temperature of the gas to T <= 78 K (T <= 115 K, 2 sigma). We used the associated CI fine structure lines to constrain the volume density of the gas, n(HI) ~ 40 - 200 cm^-3 (2 sigma), resulting in a lower limit on the cloud size of approximately 0.1 - 1 parsec. While it is difficult to determine the metallicity of the cold component, the absence of Cr II indicates that the cold cloud suffers a high level of dust depletion. Additionally, the large amount of Lyman and Werner-band molecular hydrogen absorption (log N(H2)_{total} = 19.88 cm^-2, f_{H_2} >= 0.06) with an excitation temperature of T_{ex} = 46 K as determined by the rotational J = 0 and J = 1 states, is consistent with the presence of cold gas. We propose that this cloud may be gravitationally confined and may represent a transition gas-phase from primarily neutral atomic gas, to a colder, denser molecular phase that will eventually host star formation.
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