Re-ionization of the intergalactic medium occurred in the early Universe at redshift z ~ 6-11, following the formation of the first generation of stars. Those young galaxies (where the bulk of stars formed) at a cosmic age of less than about 500 million years (z <~ 10) remain largely unexplored because they are at or beyond the sensitivity limits of existing large telescopes. Understanding the properties of these galaxies is critical to identifying the source of the radiation that re-ionized the intergalactic medium. Gravitational lensing by galaxy clusters allows the detection of high-redshift galaxies fainter than what otherwise could be found in the deepest images of the sky. Here we report multiband observations of the cluster MACS J1149+2223 that have revealed (with high probability) a gravitationally magnified galaxy from the early Universe, at a redshift of z = 9.6 +/- 0.2 (that is, a cosmic age of 490 +/- 15 million years, or 3.6 per cent of the age of the Universe). We estimate that it formed less than 200 million years after the Big Bang (at the 95 per cent confidence level), implying a formation redshift of <~14. Given the small sky area that our observations cover, faint galaxies seem to be abundant at such a young cosmic age, suggesting that they may be the dominant source for the early re-ionization of the intergalactic medium.