  Active galactic nuclei (AGN), powered by long-term accretion onto central
supermassive black holes, produce relativistic jets with lifetimes of greater
than one million yr that preclude observations at birth. Transient accretion
onto a supermassive black hole, for example through the tidal disruption of a
stray star, may therefore offer a unique opportunity to observe and study the
birth of a relativistic jet. On 2011 March 25, the Swift {\gamma}-ray satellite
discovered an unusual transient source (Swift J164449.3+573451) potentially
representing such an event. Here we present the discovery of a luminous radio
transient associated with Swift J164449.3+573451, and an extensive set of
observations spanning centimeter to millimeter wavelengths and covering the
first month of evolution. These observations lead to a positional coincidence
with the nucleus of an inactive galaxy, and provide direct evidence for a
newly-formed relativistic outflow, launched by transient accretion onto a
million solar mass black hole. While a relativistic outflow was not predicted
in this scenario, we show that the tidal disruption of a star naturally
explains the high-energy properties, radio luminosity, and the inferred rate of
such events. The weaker beaming in the radio compared to {\gamma}-rays/X-rays,
suggests that radio searches may uncover similar events out to redshifts of z ~
6.
