We report on a search for the [ C ii ] 158 \mu m emission line from galaxies associated with four high-metallicity damped Ly \alpha absorbers ( DLAs ) at z \sim 4 using the Atacama Large Millimeter/sub-millimeter Array ( ALMA ) . We detect [ C ii ] 158 \mu m emission from galaxies at the DLA redshift in three fields , with one field showing two [ C ii ] 158 \mu m emitters . Combined with previous results , we now have detected [ C ii ] 158 \mu m emission from five of six galaxies associated with targeted high-metallicity DLAs at z \sim 4 . The galaxies have relatively large impact parameters , \approx 16 - 45 kpc , [ C ii ] 158 \mu m line luminosities of ( 0.36 - 30 ) \times 10 ^ { 8 } L _ { \odot } , and rest-frame far-infrared properties similar to those of luminous Lyman-break galaxies , with star-formation rates of \approx 7 - 110 M _ { \odot } yr ^ { -1 } . Comparing the absorption and emission line profiles yields a remarkable agreement between the line centroids , indicating that the DLA traces gas at velocities similar to that of the [ C ii ] 158 \mu m emission . This disfavors a scenario where the DLA arises from gas in a companion galaxy . These observations highlight ALMA ’ s unique ability to uncover a high redshift galaxy population that has largely eluded detection for decades .