  We report a galaxy group candidate HPC1001 at $z\approx3.7$ in the COSMOS
field. This structure was selected as a high galaxy overdensity at $z>3$ in the
COSMOS2020 catalog. It contains ten candidate members, of which eight are
assembled in a $10''\times10''$ area with the highest sky density among known
protoclusters and groups at $z>3$. Four out of ten sources were also detected
at 1.2$~$mm with Atacama Large Millimeter Array continuum observations.
Photometric redshifts, measured by four independent methods, fall within a
narrow range of $3.5<z<3.9$ and with a weighted average of $z=3.65\pm0.07$. The
integrated far-IR-to-radio spectral energy distribution yields a total UV and
IR star formation rate ${\rm SFR}\approx 900~M_{\odot}~yr^{-1}$. We also
estimated a halo mass of $\sim10^{13}~M_\odot$ for the structure, which at this
redshift is consistent with potential cold gas inflow. Remarkably, the most
massive member has a specific star formation rate and dust to stellar mass
ratio of $M_{\rm dust}/M_{*}$ that are both significantly lower than that of
star-forming galaxies at this redshift, suggesting that HPC1001 could be a
$z\approx3.7$ galaxy group in maturing phase. If confirmed, this would be the
earliest structure in maturing phase to date, and an ideal laboratory to study
the formation of the earliest quiescent galaxies as well as cold gas accretion
in dense environments.
