  We measure the ages, stellar masses, and star formation histories of z~6
galaxies, observed within 1Gyr of the Big Bang. We use imaging from HST and
Spitzer from the public "Great Observatories Origins Deep Survey", coupled with
ground-based near-infrared imaging, to measure the spectral energy
distributions from 0.8-5microns, spanning the rest-frame UV and optical. From
our sample of ~50 i-drop Lyman-break star-forming galaxies in GOODS-South with
z'(AB)<27mag, we focus on ~30 with reliable photometric or spectroscopic
redshifts. Half of these are confused with foreground sources at Spitzer
resolution, but from the 16 with clean photometry we find that a surprisingly
large fraction (40%) have evidence for substantial Balmer-breaks. This
indicates the presence of old underlying stellar populations that dominate the
stellar masses. For these objects, we find ages of 200-700Myr, implying
formation redshifts of 7<z<14, and large stellar masses in the range
1-3x10^10M_sun. Analysis of 7 i-drops that are undetected at 3.6microns
indicates that these are younger, considerably less massive systems. We
calculate that line contamination should not severely affect our photometry or
derived results. Using data out to 8microns, we find little evidence for
substantial intrinsic dust reddening. Correcting for incompleteness in our
sample, we find a lower limit on the comoving stellar mass density at z~6 to be
2.5x10^6M_sun/Mpc^3. We are able to explore the star formation histories of our
selected galaxies, and we infer that the past global star formation rate may
have been much higher than that observed at z~6. The associated UV flux we
infer at z>7 could have played a major role in reionizing the universe.
