We report the detection of a z ~ 7 galaxy strongly lensed by the massive galaxy cluster A2218 (z = 0.175) at 3.6 and 4.5 μm using the Spitzer Space Telescope and at 1.1 μm using the Hubble Space Telescope. The new data indicate a refined photometric redshift in the range of 6.6-6.8 depending on the presence of Lyα emission. The spectral energy distribution is consistent with having a significant Balmer break, suggesting that the galaxy is in the poststarburst stage with an age of at least ~50 Myr and quite possibly a few hundred million years. This suggests the possibility that a mature stellar population is already in place at such a high redshift. Compared with typical Lyman break galaxies at z ~ 3-4, the stellar mass is an order of magnitude smaller (~109 M), but the specific star formation rate (star formation rate/Mstar) is similarly large (>10-9 yr-1), indicating equally vigorous star-forming activity.