We show that there has been a dramatic decline in the abundance of massive galaxies with strong Hdelta stellar absorption lines from z=1.2 to the present. These ``Hdelta-strong, or HDS, galaxies have undergone a recent and rapid break in their star-formation activity. Combining data from the Gemini Deep Deep and the Sloan Digital Sky Surveys to make mass-matched samples (M*>=10^10.2 Msun), with 25 and 50,255 galaxies, respectively), we find that the fraction of galaxies in an HDS phase has decreased from about 50% at z=1.2 to a few percent today. This decrease in fraction is due to an actual decrease in the number density of massive HDS systems by a factor of 2-4, coupled with an increase in the number density of massive galaxies by about 30 percent. We show that this result depends only weakly on the threshold chosen for the Hdelta equivalent width to define HDS systems (if greater than 4 A) and corresponds to a (1+z)^{2.5pm 0.7} evolution. Spectral synthesis studies of the high-redshift population using the PEGASE code, treating Hdelta_A, EW[OII], Dn4000, and rest-frame colors, favor models in which the Balmer absorption features in massive Hdelta-strong systems are the echoes of intense episodes of star-formation that faded about 1 Gyr prior to the epoch of observation. The z=1.4-2 epoch appears to correspond to a time at which massive galaxies are in transition from a mode of sustained star formation to a relatively quiescent mode with weak and rare star-formation episodes. We argue that the most likely local descendants of the distant massive HDS galaxies are passively evolving massive galaxies in the field and small groups.
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