We present a first analysis of deep 24 km observations with the Spitzer Space Telescope of a sample of nearly 1500 galaxies in a thin redshift slice, 0.65 , z < 0.75. We combine the infrared data with redshifts, rest-frame luminosities, and colors from COMBO-17 and with morphologies from Hubble Space Telescope images collected by the Galaxy Evolution from Morphology and SEDs (GEMS) and Great Observatories Origins Deep Survey (GOODS) projects. To characterize the decline in star formation rate (SFR) since z 6 0.7, we estimate the total thermal IR luminosities, SFRs, and stellar masses for the galaxies in this sample. At z 6 0.7, nearly 40% of intermediate- and high-mass galaxies (with stellar masses .2 x 10 super(10) M sub( )) are undergoing a period of intense star formation above their past-averaged SFR. In contrast, less than 1% of equally massive galaxies in the local universe have similarly intense star formation activity. Morphologically undisturbed galaxies dominate the total infrared luminosity density and SFR density: at z 6 0.7, more than half of the intensely star-forming galaxies have spiral morphologies, whereas less than 630% are strongly interacting. Thus, a decline in major merger rate is not the underlying cause of the rapid decline in cosmic SFR since z 6 0.7. Physical properties that do not strongly affect galaxy morphology--for example, gas consumption and weak interactions with small satellite galaxies--appear to be responsible.