We present Spitzer/IRAC observations of nine $z$-band dropouts highly magnified (2<mu<12) by the Bullet Cluster. We combine archival imaging with our Exploratory program (SURFS UP), which results in a total integration time of ~30 hr per IRAC band. We detect (>3sigma) in both IRAC bands the brightest of these high-redshift galaxies, with [3.6]=23.80+-0.28 mag, [4.5]=23.78+-0.25 mag, and (H-[3.6])=1.17+-0.32 mag. The remaining eight galaxies are undetected to [3.6]~26.4 mag and [4.5]~26.0 mag with stellar masses of ~5x10^7 M_sol. The detected galaxy has an estimated magnification of mu=12+-4, which implies this galaxy has an ultraviolet luminosity of L_1500~0.3 L*_{z=7} --- the lowest luminosity individual source detected in IRAC at z>7. By modeling the broadband photometry, we estimate the galaxy has an intrinsic star-formation rate of SFR~1.3 M_sol/yr and stellar mass of M~2x10^9 M_sol, which gives a specific star-formation rate of sSFR~0.7 Gyr^-1. If this galaxy had sustained this star-formation rate since z~20, it could have formed the observed stellar mass (to within a factor of ~2), we also discuss alternate star-formation histories and argue the exponentially-increasing model is unlikely. Finally, based on the intrinsic star-formation rate, we estimate this galaxy has a likely [C II] flux of <f_[C II]> = 10^{-17} erg/s/cm2.
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