We use a robust sample of 11 z \sim 7 galaxies ( z _ { 850 } -dropouts ) to estimate the stellar mass density of the universe when it was only \sim 750 Myr old . We combine the very deep optical to near-Infrared photometry from the HST ACS and NICMOS cameras with mid-Infrared Spitzer IRAC imaging available through the GOODS program . After carefully removing the flux from contaminating foreground sources we have obtained reliable photometry in the 3.6 \mu m and 4.5 \mu m IRAC channels . The spectral shapes of these sources , including their rest frame optical colors , strongly support their being at z \sim 7 with a mean photometric redshift of \langle z \rangle = 7.2 \pm 0.5 . We use Bruzual & Charlot ( 15 ) synthetic stellar population models to constrain their stellar masses and star formation histories . We find stellar masses that range over 0.1 - 12 \times 10 ^ { 9 } ~ { } M _ { \odot } and average ages from 20 Myr to up to 425 Myr with a mean of \sim 300 Myr , suggesting that in some of these galaxies most of the stars were formed at z > 8 ( and probably at z \gtrsim 10 ) . The best fits to the observed SEDs are consistent with little or no dust extinction , in agreement with recent results at z \sim 4 - 8 . The star formation rates ( SFR ) are in the range from 5-20 M _ { \odot } ~ { } { yr ^ { -1 } } . From this sample we measure a stellar mass density of 6.6 _ { -3.3 } ^ { +5.4 } \times 10 ^ { 5 } ~ { } M _ { \odot } ~ { } { Mpc ^ { -3 } } to a limit of M _ { UV,AB } < -20 ( or 0.4 L ^ { * } _ { z = 3 } ) . Combined with a fiducial lower limit for their ages ( 80 Myr ) this implies a maximum SFR density of 0.008 ~ { } M _ { \odot } ~ { } { yr ^ { -1 } Mpc ^ { -3 } } . This is well below the critical level needed to reionize the universe at z \sim 8 using standard assumptions . However , this result is based on luminous sources ( > L ^ { * } ) and does not include the dominant contribution of the fainter galaxies . Strikingly , we find that the specific SFR is constant from z \sim 7 to z \sim 2 but drops substantially at more recent times .