  Using the Atacama Large Millimeter/sub-millimeter Array, we have detected
CO(3-2) line and far-infrared continuum emission from a galaxy associated with
a high-metallicity ([M/H] = -0.27) damped Ly-alpha absorber (DLA) at z
=2.19289. The galaxy is located 3.5" away from the quasar sightline,
corresponding to a large impact parameter of 30 kpc at the DLA redshift. We use
archival Very Large Telescope-SINFONI data to detect Halpha emission from the
associated galaxy, and find that the object is dusty, with a dust-corrected
star formation rate of 110 +60 -30 Msun/yr. The galaxy's molecular mass is
large, Mmol = (1.4 +- 0.2) x 10^11 x (\alpha_CO/4.3) x (0.57/r_31) Msun,
supporting the hypothesis that high-metallicity DLAs arise predominantly near
massive galaxies. The excellent agreement in redshift between the CO(3-2) line
emission and low-ion metal absorption (~40 km/s) disfavors scenarios whereby
the gas probed by the DLA shows bulk motion around the galaxy. We use Giant
Metrewave Radio Telescope HI 21cm absorption spectroscopy to find that the HI
along the DLA sightline must be warm, with a stringent lower limit on the spin
temperature of T_s > 1895 x (f/0.93) K. The detection of CI absorption in the
DLA, however, also indicates the presence of cold neutral gas. To reconcile
these results requires that the cold components in the DLA contribute little to
the HI column density, yet contain roughly 50% of the metals of the absorber,
underlining the complex multi-phase nature of the gas surrounding high-z
galaxies.
