Massive galaxies in the distant Universe form stars at much higher rates than today . Although direct resolution of the star forming regions of these galaxies is still a challenge , recent molecular gas observations at the IRAM Plateau de Bure interferometer enable us to study the star formation efficiency on subgalactic scales around redshift z = 1.2 . We present a method for obtaining the gas and star formation rate ( SFR ) surface densities of ensembles of clumps composing galaxies at this redshift , even though the corresponding scales are not resolved . This method is based on identifying these structures in position-velocity diagrams corresponding to slices within the galaxies . We use unique IRAM observations of the CO ( 3-2 ) rotational line and DEEP2 spectra of four massive star forming distant galaxies - EGS13003805 , EGS13004291 , EGS12007881 , and EGS13019128 in the AEGIS terminology - to determine the gas and SFR surface densities of the identifiable ensembles of clumps that constitute them . The integrated CO line luminosity is assumed to be directly proportional to the total gas mass , and the SFR is deduced from the [ OII ] line . We identify the ensembles of clumps with the angular resolution available in both CO and [ OII ] spectroscopy ; i.e. , 1-1.5 ” . SFR and gas surface densities are averaged in areas of this size , which is also the thickness of the DEEP2 slits and of the extracted IRAM slices , and we derive a spatially resolved Kennicutt-Schmidt ( KS ) relation on a scale of \sim 8Â kpc . The data generally indicates an average depletion time of 1.9 Gyr , but with significant variations from point to point within the galaxies .