My colleagues and I identified distant red galaxies (DRGs) with J Γ K s > 2.3 in the southern Great Observatories Origins Deep Surveys (GOODS-S) field. These galaxies reside at z $ 1-3.5, (AEzae . 2.2) and based on their ACS (0.4-1 lm), ISAAC (1-2.2 lm), and IRAC (3-8 lm) photometry, they typically have stellar masses M P 10 11 M x . Interestingly, more than 50% of these objects have 24 lm flux densities P50 lJy. Attributing the IR emission to star-formation implies star-formation rates (SFRs) of .100-1000 M x yr Γ1 . As a result, galaxies with M P 10 11 M x have specific SFRs equal to or exceeding the global value at z $ 1.5-3. In contrast, galaxies with M P 10 11 M x at z $ 0.3-0.75 have specific SFRs less than the global average, and more than an order of magnitude lower than that for massive DRGs at z $ 1.5-3. Thus, the bulk of star formation in massive galaxies is largely complete by z $ 1.5. The red colors and large inferred stellar masses in the DRGs suggest that much of the star formation in these galaxies occurred at redshifts z J 5-6. Using model star-formation histories that match the DRG colors and stellar masses at z $ 2-3, and measurements of the UV luminosity density at z J 5-6, we consider what constraints exist on the stellar initial mass function in the progenitors of the massive DRGs at z $ 2-3.