  The abundance of cold molecular gas plays a crucial role in models of galaxy
evolution. While deep spectroscopic surveys of CO emission lines have been a
primary tool for measuring this abundance, the difficulty of these observations
has motivated alternative approaches to studying molecular gas content. One
technique, line intensity mapping, seeks to constrain the average molecular gas
properties of large samples of individually undetectable galaxies through the
CO brightness power spectrum. Here we present constraints on the cross-power
spectrum between CO intensity maps and optical galaxy catalogs. This
cross-measurement allows us to check for systematic problems in CO intensity
mapping data, and validate the data analysis used the auto-power spectrum
measurement of the CO Power Spectrum Survey. We place a 2-sigma upper limit on
the band-averaged CO-galaxy cross-power of $P_x<540$ uK Mpc$^3$/h$^3$. Our
measurement favors a non-zero mean CO brightness temperature at around 90%
confidence and gives an upper limit on the mean molecular gas density at z~2.6
of $7.7 \times 10^8$ Msun/Mpc$^3$. We forecast the expected cross-power
spectrum by applying a number of literature prescriptions for the CO luminosity
to halo mass relation to a suite of mock light cones. Under the most optimistic
forecasts the cross-spectrum could be detected with only moderate extensions of
the data used here, while more conservative models could be detected with a
factor of 10 increase in sensitivity. Ongoing CO intensity mapping experiments
will target fields allowing extensive cross correlation analysis and should
reach the sensitivity required to detect the cross-spectrum signal.
