We present the first photometric redshift distribution for a large sample of 870 mu m submillimeter galaxies (SMGs) with robust identifications based on observations with ALMA. In our analysis we consider 96 SMGs in the Extended Chandra Deep Field South, 77 of which have 4-19 band photometry. We model the SEDs for these 77 SMGs, deriving a median photometric redshift of z sub(phot) = 2.3 + or - 0.1. Critically we show that the proportion of galaxies undergoing an SMG-like phase at z > or =, slanted 3 is at most 35% + or - 5% of the total population. We derive a median stellar mass of M sub(*) = (8 + or - 1) x 10 super(10) M sub(middot in circle), although there are systematic uncertainties of up to 5 x for individual sources. Taken together, these results are consistent with a simple model that identifies SMGs as events that form most of the stars seen in the majority of luminous elliptical galaxies at the present day.