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.