We present constraints on the abundance of carbon-monoxide in the early Universe from the CO Power Spectrum Survey ( COPSS ) . We utilize a data set collected between 2005 and 2008 using the Sunyaev-Zel ’ dovich Array ( SZA ) , which were previously used to measure arcminute-scale fluctuations of the CMB . This data set features observations of 44 fields , covering an effective area of 1.7 square degrees , over a frequency range of 27 to 35 GHz . Using the technique of intensity mapping , we are able to probe the CO ( 1-0 ) transition , with sensitivity to spatial modes between k = 0.5 { - } 2 h \textrm { Mpc } ^ { -1 } over a range in redshift of z = 2.3 { - } 3.3 , spanning a comoving volume of 3.6 \times 10 ^ { 6 } h ^ { -3 } \textrm { Mpc } ^ { 3 } . We demonstrate our ability to mitigate foregrounds , and present estimates of the impact of continuum sources on our measurement . We constrain the CO power spectrum to P _ { \textrm { CO } } < 2.6 \times 10 ^ { 4 } \mu \textrm { K } ^ { 2 } ( h ^ { -1 } \textrm { Mpc } ) ^ { 3 } , or \Delta ^ { 2 } _ { \textrm { CO } } ( k = 1 h \textrm { Mpc } ^ { -1 } ) < 1.3 \times 10 ^ { 3 } \mu% \textrm { K } ^ { 2 } , at 95 \% confidence . This limit resides near optimistic predictions for the CO power spectrum . Under the assumption that CO emission is proportional to halo mass during bursts of active star formation , this corresponds to a limit on the ratio of \textrm { CO } ( 1 { - } 0 ) luminosity to host halo mass of A _ { \textrm { CO } } < 1.2 \times 10 ^ { -5 } L _ { \odot } M _ { \odot } ^ { -1 } . Further assuming a Milky Way-like conversion factor between CO luminosity and molecular gas mass ( \alpha _ { \textrm { CO } } = 4.3 M _ { \odot } ( \textrm { K } \textrm { km } \textrm { s } ^ { -1 } % \textrm { pc } ^ { -2 } ) ^ { -1 } ) , we constrain the global density of molecular gas to \rho _ { z \sim 3 } ( M _ { \textrm { H } _ { 2 } } ) \leq 2.8 \times 10 ^ { 8 } M _ { \odot } \textrm { % Mpc } ^ { -3 } .