We report the discovery of a unique z= 6.027 galaxy, multiply imaged by the cluster Abell 383 and detected in new Hubble Space Telescope ACS and WFC3 imaging, as well as in Warm Spitzer observations. This galaxy was selected as a pair of i-dropouts; its suspected high redshift was confirmed by the measurement of a strong Lyman α line in both images using Keck/DEIMOS. Combining Hubble and Spitzer photometry after correcting for contamination by line emission (estimated to be a small effect), we identify a strong Balmer break of 1.5 mag. Taking into account the magnification factor of 11.4 ± 1.9 (2.65 ± 0.17 mag) for the brightest image, the unlensed AB magnitude for the source is 27.2 ± 0.05 in the H band, corresponding to a 0.4 L* galaxy, and 25.7 ± 0.08 at 3.6 μm. The UV slope is consistent with β∼ 2.0, and from the rest-frame UV continuum we measure a current star formation rate of 2.4 ± 1.1 M⊙ yr−1. The unlensed half-light radius is measured to be 300 pc, from which we deduce a star-forming surface density of ∼10 M⊙ yr−1 kpc−2. The Lyman α emission is found to be extended over ∼3 arcsec along the slit, corresponding to ∼5 kpc in the source plane. This can be explained by the presence of a much larger envelope of neutral hydrogen around the star-forming region. Finally, fitting the spectral energy distribution (SED) using seven photometric data points with simple SED models, we derive the following properties: very little reddening, an inferred stellar mass of M*= 6 × 109 M⊙, and an inferred age of ∼800 Myr (corresponding to a redshift of formation of ∼18). The star formation rate of this object was likely much stronger in the past than at the time of observation, suggesting that we may be missing a fraction of galaxies at z∼ 6 which have already faded in rest-frame UV wavelengths.