We investigate the molecular gas in, and star-formation properties of, the host galaxy (CGCG 137-068) of a mysterious transient, AT2018cow, at kpc and larger scales, using archival band-3 data from the Atacama Large Millimeter/submillimeter Array (ALMA). AT2018cow is the nearest Fast-Evolving Luminous Transient (FELT), and this is the very first study unveiling molecular-gas properties of FELTs. The achieved rms and beam size are 0.21 mJy beam$^{-1}$ at a velocity resolution of $40$ km s$^{-1}$ and $3.66times2.71$ ($1.1~{rm kpc} times 0.8~{rm kpc}$), respectively. CO($J$=1-0) emission is successfully detected. The total molecular gas mass inferred from the CO data is $(1.85pm0.04)times10^8$ M$_odot$ with the Milky Way CO-to-H$_2$ conversion factor. The H$_2$ column density at the AT2018cow site is estimated to be $8.6times10^{20}$ cm$^{-2}$. The ALMA data reveal that (1) CGCG 137-068 is a normal star-forming (SF) dwarf galaxy in terms of its molecular gas and star-formation properties and (2) AT2018cow is located between a CO peak and a blue star cluster. These properties suggest on-going star formation and favor the explosion of a massive star as the progenitor of AT2018cow. We also find that CGCG 137-068 has a solar or super-solar metallicity. If the metallicity of the other FELT hosts is not higher than average, then some property of SF dwarf galaxies other than metallicity may be related to FELTs.
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