  We report the detection of the CO(2-1) emission line with a spatial
resolution of 0.9 arcsec ($3.5 \mathrm{kpc}$) from the host galaxy of the fast
radio burst (FRB), FRB 20191001A at $z=0.2340$, using the Atacama Large
Millimeter/submillimeter Array. This is the first detection of spatially
resolved CO emission from the host galaxy of an FRB at a cosmological distance.
The inferred molecular gas mass of the host galaxy is $(2.3\pm0.4)\times10^{10}
\mathrm{M_\odot}$, indicating that it is gas-rich, as evidenced by the measured
molecular gas fraction $\mu_\mathrm{gas}=0.50\pm0.22$. This molecular-gas mass
and the star formation rate of the host, $\mathrm{SFR}=8.06\pm2.42
\mathrm{M_\odot yr^{-1}}$, differ from those observed in the other FRB host
galaxies with the average $M_\mathrm{gas}=9.6\times10^8 \mathrm{M_\odot}$ and
$\mathrm{SFR}=0.90 \mathrm{M_\odot yr^{-1}}$. This lends further credibility to
the hypothesis that FRBs may originate from single or multiple progenitors
across a diverse range of galaxy environments. Based on the observed velocity
field modeling, we find that the molecular gas disk is dominated by an ordered
circular rotation, despite the fact that the host galaxy has a gas-rich
companion galaxy with a projected separation of $\sim 25 \mathrm{kpc}$. The
formation of the FRB's progenitor might not have been triggered by this
interaction. We derive the 3$\sigma$ upper limit of the molecular gas column
density at the FRB detection site to be $< 2.1\times 10^{21} \mathrm{cm^{-2}}$
with a 3$\sigma$ upper limit.
