  We present a new upper limit on the cosmic molecular gas density at
$z=2.4-3.4$ obtained using the first year of observations from the CO Mapping
Array Project (COMAP). COMAP data cubes are stacked on the 3D positions of 243
quasars selected from the Extended Baryon Oscillation Spectroscopic Survey
(eBOSS) catalog, yielding a 95% upper limit for flux from CO(1-0) line emission
of 0.129 Jy km/s. Depending on the balance of the emission between the quasar
host and its environment, this value can be interpreted as an average CO line
luminosity $L'_\mathrm{CO}$ of eBOSS quasars of $\leq 1.26\times10^{11}$ K km
pc$^2$ s$^{-1}$, or an average molecular gas density $\rho_\mathrm{H_2}$ in
regions of the universe containing a quasar of $\leq 1.52\times10^8$ M$_\odot$
cMpc$^{-3}$. The $L'_\mathrm{CO}$ upper limit falls among CO line luminosities
obtained from individually-targeted quasars in the COMAP redshift range, and
the $\rho_\mathrm{H_2}$ value is comparable to upper limits obtained from other
Line Intensity Mapping (LIM) surveys and their joint analyses. Further, we
forecast the values obtainable with the COMAP/eBOSS stack after the full 5-year
COMAP Pathfinder survey. We predict that a detection is probable with this
method, depending on the CO properties of the quasar sample. Based on the
achieved sensitivity, we believe that this technique of stacking LIM data on
the positions of traditional galaxy or quasar catalogs is extremely promising,
both as a technique for investigating large galaxy catalogs efficiently at high
redshift and as a technique for bolstering the sensitivity of LIM experiments,
even with a fraction of their total expected survey data.
