We report the detection of ADFS-27 , a dusty , starbursting major merger at a redshift of z =5.655 , using the Atacama Large Millimeter/submillimeter Array ( ALMA ) . ADFS-27 was selected from Herschel /SPIRE and APEX/LABOCA data as an extremely red ‘ ‘ 870 \mu m riser ’ ’ ( i.e. , S _ { 250 \mu { m } } < S _ { 350 \mu { m } } < S _ { 500 \mu { m } } < S _ { 870 \mu { m } } ) , demonstrating the utility of this technique to identify some of the highest-redshift dusty galaxies . A scan of the 3 mm atmospheric window with ALMA yields detections of CO ( J =5 \to 4 ) and CO ( J =6 \to 5 ) emission , and a tentative detection of H _ { 2 } O ( 2 _ { 11 } \to 2 _ { 02 } ) emission , which provides an unambiguous redshift measurement . The strength of the CO lines implies a large molecular gas reservoir with a mass of M _ { gas } =2.5 \times 10 ^ { 11 } ( \alpha _ { CO } / 0.8 ) ( 0.39 / r _ { 51 } ) M _ { \odot } , sufficient to maintain its \sim 2400 M _ { \odot } yr ^ { -1 } starburst for at least \sim 100 Myr . The 870 \mu m dust continuum emission is resolved into two components , 1.8 and 2.1 kpc in diameter , separated by 9.0 kpc , with comparable dust luminosities , suggesting an ongoing major merger . The infrared luminosity of L _ { IR } \simeq 2.4 \times 10 ^ { 13 } L _ { \odot } implies that this system represents a binary hyper-luminous infrared galaxy , the most distant of its kind presently known . This also implies star formation rate surface densities of \Sigma _ { SFR } =730 and 750 M _ { \odot } yr ^ { -1 } kpc ^ { 2 } , consistent with a binary ‘ ‘ maximum starburst ’ ’ . The discovery of this rare system is consistent with a significantly higher space density than previously thought for the most luminous dusty starbursts within the first billion years of cosmic time , easing tensions regarding the space densities of z \sim 6 quasars and massive quiescent galaxies at z \gtrsim 3 .