When an extrasolar planet passes in front of (transits) its star, its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal much more: period ratios determine stability and dynamics, mutual gravitational interactions reflect planet masses and orbital shapes, and the fraction of transiting planets observed as multiples has implications for the planarity of planetary systems. But few stars have more than one known transiting planet, and none has more than three. Here we report Kepler spacecraft observations of a single Sun-like star, which we call Kepler-11, that reveal six transiting planets, five with orbital periods between 10 and 47 days and a sixth planet with a longer period. The five inner planets are among the smallest for which mass and size have both been measured, and these measurements imply substantial envelopes of light gases. The degree of coplanarity and proximity of the planetary orbits imply energy dissipation near the end of planet formation. NASA's Kepler mission, a space observatory designed to detect and study extrasolar planets that transit across the disk of their host star, has hit the jackpot with the discovery of a six-planet system orbiting a Sun-like star now named Kepler-11. Five of the planets have orbital periods of between 10 and 47 days, and these are among the smallest for which size and mass have both been measured. The sixth and outermost transiting planet has been less well characterized thus far. Only one other star has more than one confirmed transiting planet (Kepler-9, which has three). This newly discovered system resembles our own Solar System in being close to coplanar, but Kepler-11's planets orbit much closer to their star. Kepler is due to continue to return data on Kepler-11 and its planets for some time yet, and it should provide many valuable constraints on models of the formation and evolution of solar systems in general. When an extrasolar planet passes in front of its star (transits), its radius can be measured from the decrease in starlight and its orbital period from the time between transits. This study reports Kepler spacecraft observations of a single Sun-like star that reveal six transiting planets, five with orbital periods between 10 and 47 days plus a sixth one with a longer period. The five inner planets are among the smallest for which mass and size have both been measured, and these measurements imply substantial envelopes of light gases.