  We report NOrthern Extended Millimetre Array (NOEMA) observations of warm
molecular gas traced by CO($5-4$) in a $z \sim 3.2$ gas-rich main-sequence
galaxy (MS), initially serendipitously detected in CO($3-2$) emission in
`blind' deep NOEMA observations. Our target shows a gas excitation consistent
with that seen in $z \sim 1.5$ MS galaxies ($L'_{\rm CO( 5 - 4)}/L'_{\rm CO (3
- 2)} = 0.41 \pm 0.14$), albeit toward the low end, as well as a similar star
formation efficiency based on the CO($3-2$) line luminosity and the $L_{\rm
IR}$. However, it shows a high molecular gas fraction ($f_{\rm gas} = 0.9\pm
0.2$) as compared to $z\sim 1.5$ MS galaxies ($f_{\rm gas} \sim 0.4$),
consistent with a cosmologically increasing gas fraction beyond $z\gtrsim3$ and
our current understanding of scaling relations between $z$, $f_{\rm gas}$, the
stellar mass $M_*$, and the specific star formation rate sSFR. Our results are
consistent with recent findings by the COLDz and ASPECS molecular line scan
surveys and suggest that deep searches for CO emission are a powerful means to
identify gas-rich, star-forming galaxies at high redshift.
