Active galactic nuclei (AGN) host some of the most energetic phenomena in the universe. AGN are thought to be powered by accretion of matter onto a rotating disk that surrounds a supermassive black hole. Jet streams can be boosted in energy near the event horizon of the black hole and then flow outward along the rotation axis of the disk. The mechanism that forms such a jet and guides it over scales from a few light-days up to millions of light-years remains uncertain, but magnetic fields are thought to play a critical role. Using the Atacama Large Millimeter/submillimeter Array (ALMA), we have detected a polarization signal (Faraday rotation) related to the strong magnetic field at the jet base of a distant AGN, PKS 1830–211. The amount of Faraday rotation (rotation measure) is proportional to the integral of the magnetic field strength along the line of sight times the density of electrons. The high rotation measures derived suggest magnetic fields of at least tens of Gauss (and possibly considerably higher) on scales of the order of light-days (0.01 parsec) from the black hole.