As observations of molecular gas in galaxies are pushed to lower star formation rate galaxies at higher redshifts , it is becoming increasingly important to understand the conditions of the gas in these systems to properly infer their molecular gas content . The rotational transitions of the carbon monoxide ( CO ) molecule provide an excellent probe of the gas excitation conditions in these galaxies . In this paper we present the results from the gas excitation sample of the Evolution of molecular Gas in Normal Galaxies ( EGNoG ) survey at the Combined Array for Research in Millimeter-wave Astronomy ( CARMA ) . This subset of the full EGNoG sample consists of four galaxies at z \approx 0.3 with star formation rates of 40 - 65 M _ { \odot } yr ^ { -1 } and stellar masses of \approx 2 \times 10 ^ { 11 } M _ { \odot } . Using the 3 mm and 1 mm bands at CARMA , we observe both the CO ( J = 1 \rightarrow 0 ) and CO ( J = 3 \rightarrow 2 ) transitions in these four galaxies in order to probe the excitation of the molecular gas . We report robust detections of both lines in three galaxies ( and an upper limit on the fourth ) , with an average line ratio , r _ { 31 } = L _ { \mathrm { CO ( 3 - 2 ) } } ^ { \prime } / L _ { \mathrm { CO ( 1 - 0 ) } } ^ { \prime } , of 0.46 \pm 0.07 ( with systematic errors \lesssim 40 \% ) , which implies sub-thermal excitation of the CO ( J = 3 \rightarrow 2 ) line . We conclude that the excitation of the gas in these massive , highly star-forming galaxies is consistent with normal star-forming galaxies such as local spirals , not starbursting systems like local ultra-luminous infrared galaxies . Since the EGNoG gas excitation sample galaxies are selected from the main sequence of star-forming galaxies , we suggest that this result is applicable to studies of main sequence galaxies at intermediate and high redshifts , supporting the assumptions made in studies that find molecular gas fractions in star forming galaxies at z \sim 1 - 2 to be an order of magnitude larger than what is observed locally .