We present the first detection of molecular emission from a galaxy selected to be near a projected background quasar using the Atacama Large Millimeter/submillimeter Array (ALMA). The ALMA detection of CO(1$-$0) emission from the $z=0.101$ galaxy toward quasar PKS 0439-433 is coincident with its stellar disk and yields a molecular gas mass of $M_{rm mol} approx 4.2 times 10^9 M_odot$ (for a Galactic CO-to-H$_2$ conversion factor), larger than the upper limit on its atomic gas mass. We resolve the CO velocity field, obtaining a rotational velocity of $134 pm 11$ km s$^{-1}$, and a resultant dynamical mass of $geq 4 times 10^{10} M_odot$. Despite its high metallicity and large molecular mass, the $z=0.101$ galaxy has a low star formation rate, implying a large gas consumption timescale, larger than that typical of late-type galaxies. Most of the molecular gas is hence likely to be in a diffuse extended phase, rather than in dense molecular clouds. By combining the results of emission and absorption studies, we find that the strongest molecular absorption component toward the quasar cannot arise from the molecular disk, but is likely to arise from diffuse gas in the galaxys circumgalactic medium. Our results emphasize the potential of combining molecular and stellar emission line studies with optical absorption line studies to achieve a more complete picture of the gas within and surrounding high-redshift galaxies.
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