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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 MappingArray Project (COMAP). COMAP data cubes are stacked on the 3D positions of 282quasars selected from the Extended Baryon Oscillation Spectroscopic Survey(eBOSS) catalog, yielding a 95% upper limit for flux from CO(1-0) line emissionof 0.210 Jy km/s. Depending on the assumptions made, this value can beinterpreted as either an average CO line luminosity $L'_\mathrm{CO}$ of eBOSSquasars of $\leq 7.30\times10^{10}$ K km pc$^2$ s$^{-1}$, or an averagemolecular gas density $\rho_\mathrm{H_2}$ in regions of the universe containinga quasar of $\leq 2.02\times10^8$ M$_\odot$ cMpc$^{-3}$. The $L'_\mathrm{CO}$upper limit falls among CO line luminosities obtained fromindividually-targeted quasars in the COMAP redshift range, and the$\rho_\mathrm{H_2}$ value is comparable to upper limits obtained from otherLine Intensity Mapping (LIM) surveys and their joint analyses. Further, weforecast the values obtainable with the COMAP/eBOSS stack after the full 5-yearCOMAP Pathfinder survey. We predict that a detection is probable with thismethod, depending on the CO properties of the quasar sample. Based on theseachieved sensitivities, we believe that this technique of stacking LIM data onthe positions of traditional galaxy or quasar catalogs is extremely promising,both as a technique for investigating large galaxy catalogs efficiently at highredshift and as a technique for bolstering the sensitivity of LIM experiments,even with a fraction of their total expected survey data.

COMAP Early Science: VIII. A Joint Stacking Analysis with eBOSS Quasars