We report the detection of HI 21 cm absorption from the $z=2.289$ damped Lyman-$alpha$ system (DLA) towards TXS 0311+430, with the Green Bank Telescope. The 21 cm absorption has a velocity spread (between nulls) of $sim 110$ km s$^{-1}$ and an integrated optical depth of $int tau {rm d}V = (0.818 pm 0.085)$ km s$^{-1}$. We also present new Giant Metrewave Radio Telescope 602 MHz imaging of the radio continuum. TXS 0311+430 is unresolved at this frequency, indicating that the covering factor of the DLA is likely to be high. Combining the integrated optical depth with the DLA HI column density of hi = $(2 pm 0.5) times 10^{20}$ cm, yields a spin temperature of $T_s = (138 pm 36)$ K, assuming a covering factor of unity. This is the first case of a low spin temperature ($< 350$ K) in a $z > 1$ DLA and is among the lowest ever measured in any DLA. Indeed, the $T_s$ measured for this DLA is similar to values measured in the Milky Way and local disk galaxies. We also determine a lower limit (Si/H) $gtrsim 1/3$ solar for the DLA metallicity, amongst the highest abundances measured in DLAs at any redshift. Based on low redshift correlations, the low $T_s$, large 21 cm absorption width and high metallicity all suggest that the $z sim 2.289$ DLA is likely to arise in a massive, luminous disk galaxy.
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