We report the first robust measurement of the Milky Way star formation history using the imprint left on chemical abundances of long-lived stars. The formation of the Galactic thick disk occurs during an intense star formation phase between 9.0 (z ~ 1.5) and 12.5 Gyr (z ~ 4.5) ago and is followed by a dip (at z ~ 1.1) lasting about 1 Gyr. Our results imply that the thick disk is as massive as the Milky Way's thin disk, suggesting a fundamental role of this component in the genesis of our Galaxy, something that had been largely unrecognized. This new picture implies that huge quantities of gas necessary to feed the building of the thick disk must have been present at these epochs, in contradiction with the long-term infall assumed by chemical evolution models in the last two decades. These results allow us to fit the Milky Way within the emerging features of the evolution of disk galaxies in the early universe.