The discovery of dwarf planet Eris was followed shortly by the discovery of its satellite, Dysnomia, but the satellite orbit, and thus the system mass, was not known. New observations with the Keck Observatory and the Hubble Space Telescopes show that Dysnomia has a circular orbit with a radius of 37,350 +/- 140 (1-sigma) kilometers and a 15.774 +/- 0.002 day orbital period around Eris. These orbital parameters agree with expectations for a satellite formed out of the orbiting debris left from a giant impact. The mass of Eris from these orbital parameters is 1.67 x 10(22) +/- 0.02 x 10(22) kilograms, or 1.27 +/- 0.02 that of Pluto.