We present the first direct detection of cold atomic gas in the Magellanic Stream, through 21 cm line absorption toward a background radio source, J0119–6809, using the Australia Telescope Compact Array. Two absorption components were identified at heliocentric velocities 218.6 km s–1 and 227.0 km s–1, with optical depths of τ ≈ 0.02. The corresponding H I emission region has a column density in excess of 2 × 1020 cm–2. The inferred spin temperature of the emitting gas is ~70 K. We failed to find cool gas in observations of three other radio continuum sources. Although we have definitively detected cool gas in the Stream, its spin temperature is higher than similar components in the LMC, SMC, and Bridge, and its contribution to the total H I density is probably lower. No corresponding 12CO(J = 1→ 0) or dust appears to be associated with the cool gas, suggesting that the cloud is not forming stars.