  We are undertaking an ALMA survey of molecular gas in galaxies selected for
their strong HI absorption, so-called DLA/sub-DLA galaxies. Here we report
CO(2-1) detection from a DLA galaxy at z = 0.716. We also present optical and
near-infrared spectra of the galaxy revealing [OII], H{\alpha} and [NII]
emission lines shifted by ~170 km/s relative to the DLA, and providing an
oxygen abundance 3.2 times solar, similar to the absorption metallicity. We
report low unobscured SFR ~1 Msun/yr given the large reservoir of molecular
gas, and also modest obscured SFR=4.5(+4.4,-2.6) Msun/yr based on far-IR and
sub-mm data. We determine mass components of the galaxy: log[M*/Msun] =
10.80(+0.07,-0.14), log[M mol-gas/Msun] = 10.37 +/-0.04, and log[M dust/Msun] =
8.45(+0.10,-0.30). Surprisingly, this HI absorption-selected galaxy has no
equivalent objects in CO surveys of flux-selected samples. The galaxy falls off
current scaling relations for the SFR to molecular gas mass and CO Tully-Fisher
relation. Detailed comparison of kinematical components of the absorbing,
ionized and molecular gas, combined with their spatial distribution, suggests
that part of the CO gas is both kinematically and spatially de-coupled from the
main galaxy. It is thus possible that a major star burst in the past could
explain the wide CO profile as well as the low SFR. Support for this also comes
from the SED favouring an instantaneous burst of age ~0.5 Gyr. Our survey will
establish whether flux-selected surveys of molecular gas are missing a key
stage in the evolution of galaxies and their conversion of gas to stars.
