The atmospheric Cherenkov gamma-ray telescope MAGIC, designed for a low-energy threshold, has detected very-high-energy gamma rays from a giant flare of the distant Quasi-Stellar Radio Source (in short: radio quasar) 3C 279, at a distance of more than 5 billion light-years (a redshift of 0.536). No quasar has been observed previously in very-high-energy gamma radiation, and this is also the most distant object detected emitting gamma rays above 50 gigaelectron volts. Because high-energy gamma rays may be stopped by interacting with the diffuse background light in the universe, the observations by MAGIC imply a low amount for such light, consistent with that known from galaxy counts.